Deck 4: Linear Programming: Modeling Examples

Question 1

In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤).

Answer 1

False

Question 2

When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content.

Answer 2

False

Question 3

In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store).

Answer 3

True

Question 4

A linear programming model of a media selection problem is used to determine the relative value of each advertising media.

Question 5

Solutions to diet problems in linear programming are always realistic.

Question 6

Transportation problems can have solution values that are non-integer and must be rounded.

Question 7

In an unbalanced transportation model, supply does not equal demand, and supply constraints have ≤ signs.

Question 8

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure.

Question 9

Product mix problems cannot have greater-than-or-equal-to (≥) constraints.

Question 10

In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill).

Question 11

Diet problems usually maximize nutritional value.

Question 12

The constraint x + y = z is written in standard form.

Question 13

In a transportation problem, a supply constraint (the maximum amount of product available for shipment or distribution at a given source) is a greater-than-or equal-to constraint (≥).

Question 14

In a media selection problem, maximization of audience exposure may not result in maximization of total profit.

Question 15

When using a linear programming model to solve the diet problem, the objective is generally to maximize profit.

Question 16

In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories.

Question 17

Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.

Question 18

In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

Question 19

In most media selection decisions, the objective of the decision maker is to minimize cost.

Question 20

A conservative approach to a balanced transportation model would be to make all constraints less-than-or-equal-to constraints.

Question 21

Data envelopment analysis indicates the relative ________ of a service unit compared with others.

Question 22

________ types of linear programming problems often result in fractional relations between variables which must be eliminated.

Question 23

Fractional relationships among variables are considered standard form in a blending problem.

Question 24

Cranky Jerry's Day Care wants to minimize their food cost while meeting the minimum (and I mean bare minimum) guidelines for nutrition as set forth by the state. The best approach would be to follow the example in this chapter for a(n) ________ problem.

Question 25

Investment problems maximize ________.

Question 26

When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are mutliplied by the values in another column (or row) and then summed.

Question 27

A balanced transportation model should have ________ constraints.

Question 28

In a balanced transportation model, supply equals ________.

Question 29

Data envelopment analysis indicates which type of service unit makes the highest profit.

Question 30

In a classic blending problem, revenue is maximized by subtracting cost from profit.

Question 31

Data envelopment analysis problems are usually maximization problems.

Question 32

The objective function of a diet problem is usually to ________ subject to nutritional requirements.

Question 33

Blending problems usually require algebraic manipulation in order to write the LP in "standard form."

Question 34

In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit.

Question 35

The ________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.

Question 36

Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter.

Question 37

An unbalanced transportation model must have at least one ________ constraint.

Question 38

For product mix problems, the constraints are usually associated with ________.

Question 39

There are three plants scattered across the United States that manufacture Dull computers. These plants assemble products for customers throughout the United States, Canada, and Mexico. If Dull wishes to maximize profit by choosing the most economical pair of factory and customer for each order, they would be well-advised to follow the ________ model presented in this chapter.

Question 40

In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________.

Question 41

Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows:
Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan, and how much fat and protein do the cats receive?

Question 42

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.
What is a full set of constraints if the farmer wants this flock to produce less than 100 decibels of noise and more than 5 pounds of fertilizer, consume less than 10 pounds of layer pellets, and achieve a total plumage score of at least 75?

Question 43

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50.
For the production combination of 800 bags of lime and 600 bags of vinegar, which resource is not completely used up and how much is remaining?

Question 44

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each.

-What is the formulation for this problem?

Question 45

For the production combination of 600 bear claws and 800 almond-filled croissants, how much flour and almond paste are remaining?

Question 46

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50.

-What is the formulation for this problem?

Question 47

The poultry farmer discovers, much to his dismay, that the product mix that satisfies all of his constraints isn't really a mix of birds--it's a flock consisting of nothing but 32 Leghorns. (His constraints were a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperment less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week.) Not only is his flock going to be a very one-note mix in terms of color, he is afraid that the gleaming white feathers and deafening noise will attract predators, or worse yet, his neighbors. He immediately embarks on a breeding program to develop a Super-Cochin that can lay 4.5 eggs per week with all other performance measures the same. His optimal solution is now 27.5 Leghorns and 5.625 Super-Cochins. Assuming that he is willing to settle for a flock that has 27 Leghorns and 5 Super Cochins, what is the weekly output of eggs and performance with respect to the constraints?

Question 48

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.
How should the objective function read?

Question 49

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week.
The table below shows relevant manufacturing information:

Write the constraints for the total number of shirts of each style produced.

Question 50

Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard wheels and 1200 deluxe wheels for next month, and for 750 standard wheels and 1000 deluxe wheels the following months. He must fill all the orders. The cost of regular time production for standard wheels is $25 and for deluxe wheels, $40. Overtime production costs 50% more. For each of the next two months there are 1000 hours of regular time production and 500 hours of overtime production available. A standard wheel requires .5 hour of production time and a deluxe wheel, .6 hour. The cost of carrying a wheel from one month to the next is $2.

-Write the constraints for this problem.

Question 51

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week.
The table below shows relevant manufacturing information:

Assume that the decision variables are defined as follows:
A = total number of athletic shirts produced
V = total number of varsity shirts produced
S = total number of surfer shirts produced
C = yards of cotton purchased
R = yards of rayon purchased
Xij = yards of fabric i (C or R) blended into shirt j (A, V or S)
Write the objective function.

Question 52

Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard wheels and 1200 deluxe wheels for next month, and for 750 standard wheels and 1000 deluxe wheels the following months. He must fill all the orders. The cost of regular time production for standard wheels is $25 and for deluxe wheels, $40. Overtime production costs 50% more. For each of the next two months there are 1000 hours of regular time production and 500 hours of overtime production available. A standard wheel requires .5 hour of production time and a deluxe wheel, .6 hour. The cost of carrying a wheel from one month to the next is $2.
Define the decision variables and objective function for this problem.

Question 53

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.
Formulate the objective function and constraints for this scenario.

Question 54

If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company's three products in period 2 is 400.

Question 55

Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How much oil-based and water-based paint should the Quickbrush make?

Question 56

Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week.
The table below shows relevant manufacturing information:

Write the constraints for the fabric requirements.

Question 57

In a(n) ________ transportation problem, supply exceeds demand.

Question 58

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50.
The production combination of 450 bags of lime and 800 bags of vinegar is not feasible because one resource is exceeded. Which resource is exceeded and how much more is needed to produce this combination?

Question 59

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each.
This represents what type of linear programming application?

Question 60

Small motors for garden equipment are produced at four manufacturing facilities and need to be shipped to three plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the three different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility.

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { To Plant }$
$\begin{array}{crrrrr}\text{From Manufacturing Facility} &&A & B & C & Supply\\\hline 1 & & 4 & 4.5 & 3.2 & 200 \\2 & & 3.5 & 3 & 4 & 200 \\3 & & 4 & 3.5 & 4.25 & 300 \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { Demand } && 250 & 150 & 200 &\end{array}$


Write the formulation for this problem.

Question 61

The production manager for the Softy soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit?

A) $270
B) $320
C) $420
D) $520

Question 62

Balanced transportation problems have the following type of constraints:

A) ≥
B) ≤
C) =
D) <

Question 63

Compared to blending and product mix problems, transportation problems are unique because

A) they maximize profit.
B) the constraints are all equality constraints with no "≤" or "≥" constraints.
C) they contain fewer variables.
D) the solution values are always integers.

Question 64

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1.

A) x21 + x22 ≤ 8000
B) x12 + x22 ≥ 8000
C) x11 + x12 ≤ 8000
D) x21 + x22 ≥ 8000

Question 65

A credit union wants to make investments in the following:
The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply:
∙ Risk-free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total.
∙ Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans)
∙ Consumer loans plus other secured loans may not exceed the vehicle loans
∙ Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.
How should the $2,500,000 be allocated to each alternative to maximize annual return? What is the annual return?

Question 66

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50.
Which of the following is not a feasible production combination?

A) 0L and 0V
B) 0L and 1000V
C) 1000L and 0V
D) 0L and 1200V

Question 67

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50.
What is the constraint for salt?

A) 6L + 8V ≤ 4800
B) 1L + 2V ≤ 4800
C) 3L + 2V ≤ 4800
D) 2L + 3V ≤ 4800

Question 68

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit?

A) $380
B) $400
C) $420
D) $440

Question 69

When systematically formulating a linear program, the first step is to

A) construct the objective function.
B) formulate the constraints.
C) identify the decision variables.
D) identify the parameter values.

Question 70

Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2". The constraint for this requirement can be written as:

A) x2 ≥ .60
B) x2 ≥ .60 (x2 + x7 + x8)
C) )4x2 - .6x7 - .6x8 ≤ 0
D) )4x2 - .6x7 - .6x8 ≥ 0

Question 71

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.
$$\begin{array} { | l | c | c | c | } \hline \text { Bird } & \text { Leghorn } & \text { Cochin } & \text { Buff Orpington } \\\hline \text { Eggs/week } & 5 & 2 & 4.5 \\\hline \text { Plumage } & 3 & 9 & 6 \\\hline \text { Temperment } & 2 & 8 & 5 \\\hline \text { Fertilizer } & 3 & 2 & 4 \\\hline \text { Appetite } & 5 & 4 & 8 \\\hline\end{array}$$ Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.

-Which of the following is an appropriate objective function?

A) Max Z = 5L + 2C + 4.5B
B) Max Z = 10L + 10C + 10B
C) Min Z = 5L + 2C + 4.5B
D) Min Z = 10L + 10C + 10B

Question 72

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.
$$\begin{array} { | l | c | c | c | } \hline \text { Bird } & \text { Leghorn } & \text { Cochin } & \text { Buff Orpington } \\\hline \text { Eggs/week } & 5 & 2 & 4.5 \\\hline \text { Plumage } & 3 & 9 & 6 \\\hline \text { Temperment } & 2 & 8 & 5 \\\hline \text { Fertilizer } & 3 & 2 & 4 \\\hline \text { Appetite } & 5 & 4 & 8 \\\hline\end{array}$$ Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.

-The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperment less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. When he runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He can picture the sad little faces of his children when he tells them that there will be no variety of birds gracing their front lawn this summer. Help him avoid the embarrassment by selecting a constraint that will ensure that there is some variety in his flock.

A) 5L + 4C + 8B ? 160
B) 5L + 4C + 8B ? 160
C) C + B ? 5
D) L + C + B ? 5

Question 73

When the poultry farmer runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He studies his sensitivity report (copied below) and decides to write a constraint that requires two Cochin chickens to be selected. If the current optimal mix of breeds results in 160 eggs per week, which of the following statements is best?

A) The new weekly egg output will be 169.
B) The new weekly egg output will be 162.
C) The new weekly egg output will be 158.
D) The new weekly egg output will be 153.

Question 74

The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperment less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. Use this portion of the sensitivity report to evaluate the following statements:

A) The noise level around the farm should be over 60 decibels.
B) The fertilizer generated will be 160 ounces per week.
C) Layer pellets will be consumed at the rate of 96 ounces per week.
D) The plumage score will be less than 40.

Question 75

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50.
For the production combination of 800 bags of lime and 600 bags of vinegar, which of the three resources is (are) not completely used?

A) flour only
B) salt only
C) herbs only
D) salt and flour

Question 76

If Xab = the production of product a in period b, then to indicate that the limit on production of the company's 3 products in period 2 is 400, we write:

A) X32 ≤ 400
B) X21 + X22 + X23 ≤ 400
C) X12 + X22 + X32 ≤ 400
D) X12 + X22 + X32 ≥ 400

Question 77

The production manager for the Softy soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

A) 2R + 4D ≤ 480
B) 2D + 4R ≤ 480
C) 2R + 3D ≤ 480
D) 3R + 2D ≤ 480

Question 78

The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B, which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.
$$\begin{array} { | l | l | l | l | } \hline & \text { Percent per } & \text { Percent per } & \begin{array} { l } \text { Minimum daily } \\\text { requirement }\end{array} \\\text { Ingredient}&\text {pound in Feed A}&\text { pound in Feed B } & \text { (pounds) } \\\hline 1 & 20 & 24 & 30 \\\hline 2 & 30 & 10 & 50 \\\hline 3 & 0 & 30 & 20 \\\hline 4 & 24 & 15 & 60 \\\hline 5 & 10 & 20 & 40 \\\hline\end{array}$$
The constraint for ingredient 3 is:

A) .5A + .75B = 20
B) .3B = 20
C) .3B? 20
D) .3B ? 20

Question 79

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.
$$\begin{array} { | l | c | c | c | } \hline \text { Bird } & \text { Leghorn } & \text { Cochin } & \text { Buff Orpington } \\\hline \text { Eggs/week } & 5 & 2 & 4.5 \\\hline \text { Plumage } & 3 & 9 & 6 \\\hline \text { Temperment } & 2 & 8 & 5 \\\hline \text { Fertilizer } & 3 & 2 & 4 \\\hline \text { Appetite } & 5 & 4 & 8 \\\hline\end{array}$$ Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.

-The poultry farmer would like to generate 80 ounces of fertilizer per week while feeding a maximum of 160 ounces of layer pellets each week. Which of these constraints is correct?

A) 3L + 2C + 4C ? 80
B) 5L + 4C + 8B ? 160
C) 5L + 4C + 8B ? 160
D) 5L + 4C +8B ? 80

Question 80

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the demand constraint for gasoline type 1.

A) x21 + x22 = 11000
B) x12 + x22 = 11000
C) x11 + x21 ≤ 11000
D) x11 + x21 = 11000