Deck 9: Linear Programming

Question 1

An example of a decision variable in an LP problem is profit maximization.

Answer 1

False

Question 2

Every constraint in a maximization problem has a slack variable.

Answer 2

False

Question 3

A linear programming problem can have multiple optimal solutions.

Answer 3

True

Question 4

The value of an objective function decreases as it is moved away from the origin.

Question 5

The term "isoprofit" line means that all points on the line will yield the same profit.

Question 6

Linear programming techniques will produce an optimal solution to problems that involve limitations on resources.

Question 7

The graphical Solution Method can handle problems that involve any number of decision variables.

Question 8

The equation 5x + 7y = 10 is linear.

Question 9

For a nonbinding constraint,if the left side is greater than the right side,we say that there is surplus; if the left side is smaller than the right side,we say that there is slack.

Question 10

LP problems must have a single goal or objective specified.

Question 11

Constraints limit the alternatives available to a decision-maker.

Question 12

The feasible solution space is the set of all feasible combinations of decision variables as defined by only binding constraints.

Question 13

If a single optimal solution exists to a graphical LP problem,it will exist at a corner point.

Question 14

A maximization problem may be characterized by all greater than or equal to constraints.

Question 15

A change in the value of an objective function coefficient does not change the optimal solution.

Question 16

The simplex method is an LP algorithm that can solve problems having more than two decision variables.

Question 17

The removal of a redundant constraint does not affect the feasible solution space.

Question 18

The feasible solution space only contains points that satisfy all constraints.

Question 19

The equation 3xy = 9 is linear.

Question 20

An objective function represents a family of parallel lines.

Question 21

The region which satisfies all of the constraints in linear programming is called the:

A)optimum solution space.
B)region of optimality.
C)profit maximization space.
D)region of non-negativity.
E)feasible solution space.

Question 22

In the range of feasibility,the value of the shadow price remains constant.

Question 23

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

Question 24

The linear optimization technique for allocating constrained resources among different products is:

A)linear regression analysis.
B)linear disaggregation.
C)linear decomposition.
D)linear programming.
E)linear tracking analysis.

Question 25

A shadow price indicates how much a one-unit decrease/increase in the right-hand side value of a constraint will decrease/increase the optimal value of the objective function.

Question 26

Which of the following is not a necessary assumption in order for a linear programming model to be used effectively?

A)Linearity
B)Exponentiality
C)Divisibility
D)Certainty
E)Non-negativity

Question 27

In graphical linear programming the objective function is:

A)linear,one equation based,a family of its profit lines
B)a family of parallel lines,linear,both linear and nonlinear
C)a family of is profit lines,linear on the right,nonlinear on the left
D)a family of is profit lines,a family of parallel lines,nonlinear
E)linear,a family of parallel lines,a family of is profit lines

Question 28

The logical approach,from beginning to end,for assembling a linear programming model begins with:

A)identifying the decision variables.
B)identifying the objective function.
C)specifying the objective function parameters.
D)identifying the constraints.
E)specifying the constraint parameters.

Question 29

Which objective function has the same slope as this one: $4x + $2y = $20?

A)$4x + $2y = $10
B)$2x + $4y = $20
C)$2x - $4y = $20
D)$4x - $2y = $20
E)$8x + $8y = $20

Question 30

Which of the following is not written in the standard form of a linear programming problem constraint?

A)1A + 2B $\ge$ 3
B)1A + 2B $\le$ 3
C)1A + 2B = 3
D)1A + 2B + 3C + 4D $\le$ 5
E)2A $\le$ 3B

Question 31

What combination of x and y will yield the optimum solution for this problem? Maximize Z = $3x + $15y; Subject to: (1)2x + 4y $\le$ 12 (2)5x + 2y $\le$ 10

A)x = 2,y = 0
B)x = 0,y = 0
C)x = 0,y = 3
D)x = 1,y = 5
E)x = 1,y = 3

Question 32

For the products A,B,C,and D,which of the following could be a linear programming objective function?

A)Z = 1A + 2B + 3C + 4D
B)Z = 1A + 2BC + 3D
C)Z = 1A + 2AB + 3ABC + 4ABCD
D)Z = 1A + 2B/C + 3D

Question 33

Which of the choices below constitutes a simultaneous solution to these equations? (1)3x + 2y = 6 and (2)6x + 3y = 12

A)x = 1,y = 1.5
B)x = .5,y = 2
C)x = 0,y = 3
D)x = 2,y = 0
E)x = 0,y = 0

Question 34

In the graphical solution method for minimization problems,we find the optimal corner point by sliding the objective function line (which is an isocost line)toward the origin instead of away from it.

Question 35

Which of the choices below constitutes a simultaneous solution to these equations? (1)3x + 4y = 10 and (2)5x + 4y = 14

A)x = 2,y = .5
B)x = 4,y = -.5
C)x = 2,y = 1
D)x = y
E)y = 2x

Question 36

The term "range of optimality" refers to a range of values for an objective function coefficient over which the optimal solution values of the decision variables remain the same.

Question 37

For the constraints given below,which point is in the feasible solution space of this maximization problem? (1)14x + 6y $\le$ 42
(2)x - y $\le$ 3

A)x = 1,y = 5
B)x = -1,y = 1
C)x = 4,y = 4
D)x = 2,y = 1
E)x = 2,y = 8

Question 38

The term "range of feasibility" refers to coefficients of the objective function.

Question 39

When a change in the value of an objective function coefficient remains within the range of optimality,the optimal solution would also remain the same.

Question 40

Which of the following is not a component of the structure of a linear programming model?

A)Constraints
B)Decision variables
C)Environment of certainty
D)A goal or objective
E)Parameters

Question 41

The operations manager for the Blue Moon Brewing Co.produces two beers: Lite (L)and Dark (D).Two of his resources are constrained: production time,which is limited to 8 hours (480 minutes)per day; and malt extract (one of his ingredients),of which he can get only 675 gallons each day.To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract,while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract.Profits for Lite beer are $3.00 per keg,and profits for Dark beer are $2.00 per keg.What is the time constraint?

A)2 L + 3 D $\le$ 480
B)2 L + 4 D $\le$ 480
C)3 L + 2 D $\le$ 480
D)4 L + 2 D $\le$ 480
E)5 L + 3 D $\le$ 480

Question 42

The operations manager for the Blue Moon Brewing Co.produces two beers: Lite (L)and Dark (D).Two of his resources are constrained: production time,which is limited to 8 hours (480 minutes)per day; and malt extract (one of his ingredients),of which he can get only 675 gallons each day.To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract,while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract.Profits for Lite beer are $3.00 per keg,and profits for Dark beer are $2.00 per keg.What are optimal daily profits?

A)$0
B)$240
C)$420
D)$405
E)$505

Question 43

The operations manager for the Blue Moon Brewing Co.produces two beers: Lite (L)and Dark (D).Two of his resources are constrained: production time,which is limited to 8 hours (480 minutes)per day; and malt extract (one of his ingredients),of which he can get only 675 gallons each day.To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract,while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract.Profits for Lite beer are $3.00 per keg,and profits for Dark beer are $2.00 per keg.What is the objective function?

A)Z = $2 L + $3 D
B)Z = $2 L + $4 D
C)Z = $3 L + $2 D
D)Z = $4 L + $2 D
E)Z = $5 L + $3 D

Question 44

In the graphical method of linear programming,when the objective function is parallel to one of the constraints,then:

A)the solution is suboptimal.
B)multiple optimal solutions exist.
C)a single corner point solution exists.
D)no feasible solution exists.
E)the constraints need to be changed

Question 45

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.Using the graphical method,what are optimal weekly profits?

A)$0
B)$400
C)$700
D)$800
E)$900

Question 46

The operations manager for the Blue Moon Brewing Co.produces two beers: Lite (L)and Dark (D).Two of his resources are constrained: production time,which is limited to 8 hours (480 minutes)per day; and malt extract (one of his ingredients),of which he can get only 675 gallons each day.To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract,while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract.Profits for Lite beer are $3.00 per keg,and profits for Dark beer are $2.00 per keg.Which of the following is not a feasible production combination?

A)0 L & 0 D
B)0 L & 120 D
C)90 L & 75 D
D)135 L & 0 D
E)135 L & 120 D

Question 47

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.For the production combination of 0 American and 400 British,which resource is "slack" (not fully used)?

A)Colombian beans (only)
B)Dominican beans (only)
C)Both Colombian beans and Dominican beans
D)Neither Colombian beans nor Dominican beans
E)Cannot be determined exactly

Question 48

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:

A)1
B)2
C)3
D)4
E)unlimited.

Question 49

What is the linear programming approach where substituting the coordinates of each corner point into the objective function determines the corner point which is optimal?

A)redundant constraints
B)binding constraints
C)surplus
D)slack constraints
E)enumeration

Question 50

In linear programming,sensitivity analysis is associated with:

A)A constraint that forms the optimal corner point of the feasible solution space.
B)Substituting the coordinates of each corner point into the objective function to determine which corner point is optimal.
C)Assessing the impact of potential changes of the parameters (numerical values)of an LP model on its optimal solution.
D)A constraint that does not form a unique boundary of the feasible solution space.
E)Representing the requirements or limitations that restrict the available choices.

Question 51

Which graphical solution method finds the optimal corner point by sliding the objective function line (which is an isocost line)toward the origin instead of away from it?

A)surplus
B)slack
C)maximization
D)minimization
E)simplex

Question 52

For the constraints given below,which point is in the feasible solution space of this minimization problem? (1)14x + 6y > 42 (2)x + 3y > 6

A)x = 0.5,y = 5.0
B)x = 0.0,y = 4.0
C)x = 2.0,y = 5.0
D)x = 1.0,y = 2.0
E)x = 2.0,y = 1.0

Question 53

A shadow price reflects which of the following in a maximization problem?

A)The marginal cost of adding additional resources
B)The marginal gain in the objective that would be realized by adding one unit of a resource
C)The net gain in the objective that would be realized by adding one unit of a resource
D)The marginal gain in the objective that would be realized by subtracting one unit of a resource
E)Assessing the impact of potential changes of the parameters (numerical values)of an LP model on its optimal solution.

Question 54

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.Which of the following is not a feasible production combination?

A)0 A & 0 B
B)0 A & 400 B
C)200 A & 300 B
D)400 A & 0 B
E)400 A & 400 B

Question 55

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.What is the Dominican bean constraint?

A)12A + 8B $\le$ 4,800
B)8A + 12B $\le$ 4,800
C)4A + 8B $\le$ 3,200
D)8A + 4B $\le$ 3,200
E)4A + 8B $\le$ 4,800

Question 56

The operations manager for the Blue Moon Brewing Co.produces two beers: Lite (L)and Dark (D).Two of his resources are constrained: production time,which is limited to 8 hours (480 minutes)per day; and malt extract (one of his ingredients),of which he can get only 675 gallons each day.To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract,while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract.Profits for Lite beer are $3.00 per keg,and profits for Dark beer are $2.00 per keg.For the production combination of 135 Lite and 0 Dark,which resource is "slack" (not fully used)?

A)Time (only)
B)Malt extract (only)
C)Both time and malt extract
D)Neither time nor malt extract
E)Cannot be determined exactly

Question 57

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.What is the objective function?

A)Z = $1 A + $2 B
B)Z = $12 A + $8 B
C)Z = $2 A + $1 B
D)Z = $8 A + $12 B
E)Z = $4 A + $8 B

Question 58

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Colombia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.What is the Colombian bean constraint?

A)1 A + 2 B $\le$ 4,800
B)12 A + 8 B $\le$ 4,800
C)2 A + 1 B $\le$ 4,800
D)8 A + 12 B $\le$ 4,800
E)4 A + 8 B $\le$ 4,800

Question 59

What combination of x and y will provide a minimum for this problem? Minimize Z = $3x + $15y; Subject to: (1)2x + 4y > 12 (2)5x + 2y > 10

A)x = 0,y = 0
B)x = 0,y = 3
C)x = 0,y = 5
D)x = 1,y = 2.5
E)x = 6,y = 0

Question 60

A constraint that does not form a unique boundary of the feasible solution space is a:

A)redundant constraint.
B)binding constraint.
C)non-binding constraint.
D)feasible solution constraint.
E)variable constraint

Question 61

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.What is the constraint for sugar?

A)2 D + 3 C $\le$ 4,800
B)6 D + 8 C $\le$ 4,800
C)1 D + 2 C $\le$ 4,800
D)3 D + 2 C $\le$ 4,800
E)4 D + 5 C $\le$ 4,800

Question 62

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.What is the objective function?

A)Z = $4 R + $6 S
B)Z = $2 R + $3 S
C)Z = $6 R + $4 S
D)Z = $3 R + $2 S
E)Z = $5 R + $5 S

Question 63

An electronics firm produces two models of pocket calculators: the A-100 (A),which is an inexpensive four-function calculator,and the B-200 (B),which also features square root and percent functions.Each model uses one (the same)circuit board,of which there are only 2,500 available for this week's production.Also,the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators,of which the A-100 requires 15 minutes (.25 hours)each,and the B-200 requires 30 minutes (.5 hours)each to produce.The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.What are optimal weekly profits?

A)$10,000
B)$4,600
C)$2,500
D)$5,200
E)$6,400

Question 64

An electronics firm produces two models of pocket calculators: the A-100 (A),which is an inexpensive four-function calculator,and the B-200 (B),which also features square root and percent functions.Each model uses one (the same)circuit board,of which there are only 2,500 available for this week's production.Also,the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators,of which the A-100 requires 15 minutes (.25 hours)each,and the B-200 requires 30 minutes (.5 hours)each to produce.The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.For the production combination of 1,400 A-100's and 900 B-200's,which resource is "slack" (not fully used)?

A)Circuit boards (only)
B)Assembly time (only)
C)Both circuit boards and assembly time
D)Neither circuit boards nor assembly time
E)Cannot be determined exactly

Question 65

An electronics firm produces two models of pocket calculators: the A-100 (A),which is an inexpensive four-function calculator,and the B-200 (B),which also features square root and percent functions.Each model uses one (the same)circuit board,of which there are only 2,500 available for this week's production.Also,the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators,of which the A-100 requires 15 minutes (.25 hours)each,and the B-200 requires 30 minutes (.5 hours)each to produce.The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.What is the assembly time constraint (in hours)?

A)1 A + 1 B $\le$ 800
B)0.25 A + 0.5 B $\le$ 800
C)0.5 A + 0.25 B $\le$ 800
D)1 A + 0.5 B $\le$ 800
E)0.25 A + 1 B $\le$ 800

Question 66

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.For the production combination of 180 Root beer and 0 Sassafras sodas,which resource is "slack" (not fully used)?

A)Production time (only)
B)Carbonated water (only)
C)Both production time and carbonated water
D)Neither production time nor carbonated water
E)Cannot be determined exactly

Question 67

An electronics firm produces two models of pocket calculators: the A-100 (A),which is an inexpensive four-function calculator,and the B-200 (B),which also features square root and percent functions.Each model uses one (the same)circuit board,of which there are only 2,500 available for this week's production.Also,the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators,of which the A-100 requires 15 minutes (.25 hours)each,and the B-200 requires 30 minutes (.5 hours)each to produce.The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.What is the objective function?

A)Z = $4.00 A + $1.00 B
B)Z = $0.25 A + $1.00 B
C)Z = $1.00 A + $4.00 B
D)Z = $1.00 A + $1.00 B
E)Z = $0.25 A + $0.50 B

Question 68

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.Using the graphical method,what are optimal daily profits?

A)$960
B)$1,560
C)$1,800
D)$1,900
E)$2,520

Question 69

An electronics firm produces two models of pocket calculators: the A-100 (A),which is an inexpensive four-function calculator,and the B-200 (B),which also features square root and percent functions.Each model uses one (the same)circuit board,of which there are only 2,500 available for this week's production.Also,the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators,of which the A-100 requires 15 minutes (.25 hours)each,and the B-200 requires 30 minutes (.5 hours)each to produce.The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.Which of the following is not a feasible production/sales combination?

A)0 A & 0 B
B)0 A & 1,000 B
C)1,800 A & 700 B
D)2,500 A & 0 B
E)100 A & 1,600 B

Question 70

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.What is the objective function?

A)Z = $0.30 B + $0.20 C
B)Z = $0.60 B + $0.30 C
C)Z = $0.20 B + $0.30 C
D)Z = $0.20 B + $0.40 C
E)Z = $0.10 B + $0.10 C

Question 71

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.Which of the following is not a feasible production combination?

A)0 D & 0 C
B)0 D & 1,000 C
C)800 D & 600 C
D)1,600 D & 0 C
E)0 D & 1,200 C

Question 72

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.Using the graphical method,what are optimal profits for today's production run?

A)$580
B)$340
C)$220
D)$380
E)$420

Question 73

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.What is the production time constraint (in minutes)?

A)2 R + 3 S $\le$ 720
B)2 R + 5 S $\le$ 720
C)3 R + 2 S $\le$ 720
D)3 R + 5 S $\le$ 720
E)5 R + 5 S $\le$ 720

Question 74

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.What is the sugar constraint (in tablespoons)?

A)6 B + 3 C $\le$ 4,800
B)1 B + 1 C $\le$ 4,800
C)2 B + 4 C $\le$ 4,800
D)4 B + 2 C $\le$ 4,800
E)2 B + 3 C $\le$ 4,800

Question 75

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.Using the graphical method,what are profits for the optimal production combination?

A)$800
B)$500
C)$640
D)$620
E)$600

Question 76

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.Which of the following is not a feasible production combination?

A)0 B & 0 C
B)0 B & 1,100 C
C)800 B & 600 C
D)1,100 B & 0 C
E)0 B & 1,400 C

Question 77

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.Which of the following is not a feasible production combination?

A)0 R & 0 S
B)0 R & 240 S
C)180 R & 120 S
D)300 R & 0 S
E)180 R & 240 S

Question 78

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.For the production combination of 800 boxes of Deluxe and 600 boxes of Classic,which resource is slack (not fully used)?

A)Sugar (only)
B)Flour (only)
C)Salt (only)
D)Sugar and flour
E)Sugar and salt

Question 79

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.What is the objective function?

A)Z = $0.50 D + $0.40 C
B)Z = $0.20 D + $0.30 C
C)Z = $0.40 D + $0.50 C
D)Z = $0.10 D + $0.20 C
E)Z = $0.60 D + $0.80 C

Question 80

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.For the production combination of 600 bagels and 800 croissants,which resource is "slack" (not fully used)?

A)Flour (only)
B)Sugar (only)
C)Flour and yeast
D)Flour and sugar
E)Yeast and sugar