Question 1

Scenario D.1
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
-Referring to Scenario D.1, what is an appropriate constraint for this scenario?
A) 4*Eggs + 5*Tomatoes + 14*Chicken ≥ 15
B) 22*Protein + 15*VitaminA + 8*VitaminB ≥ 8
C) .12*Egg + .5*Tomato + .4*Chicken ≥ 4
D) 22*Protein + 15*VitaminA + 8*VitaminB ≥ 4

Accepted Answer

The correct constraint for ensuring the minimum requirement of vitamin A (15 units) in a 4-ounce portion using the ingredients provided would be based on the vitamin A content per ounce of each ingredient. Since eggs provide 4 units of Vitamin A per ounce, tomatoes provide 5 units, and chicken provides 14 units, the constraint to meet the vitamin A requirement would be 4*Eggs + 5*Tomatoes + 14*Chicken ≥ 15.

Question 2

The ________ problem is a one-period type of aggregate planning problem, the solution of which yields optimal output quantities of a group of products or services, subject to resource capacity and market demand conditions.

Accepted Answer

The answer of The ________ problem is a one-period type...

Question 3

Scenario D.1
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
-Referring to Scenario D.1, assume that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes. Which of the following statements is best?
A) The serving costs about 20 cents.
B) The serving costs about 30 cents
C) The serving costs about 40 cents.
D) The serving costs about 50 cents.

Accepted Answer

To find the cost of the serving, we need to calculate the cost of 0.89 ounces of chicken and 0.52 ounces of tomatoes.

The cost of 0.89 ounces of chicken is 0.89 x 40 = 35.6 cents
The cost of 0.52 ounces of tomatoes is 0.52 x 8 = 4.16 cents
Total cost = 35.6 + 4.16 = 39.76 cents

Therefore, the best choice is C, "The serving costs about 40 cents."

Question 4

When plotting constraints, it is best to ignore the inequality aspect of the equation.

Accepted Answer

When plotting constraints, it is best to ignore the inequality aspect of the equation because the inequality is already represented by the direction of the line.

Question 5

An equality constraint requires that only the points on the line described by the constraint are feasible.

Accepted Answer

This is because an equality constraint sets the value of one variable equal to a constant value, making only the points on the line (or hyperplane in higher dimensions) feasible solutions. Points off the line will not satisfy the constraint and thus cannot be optimal solutions.

Question 6

Belsky Manufacturing makes three models of fans, identified by the unimaginative names of A, B, and C. The fans are made out of nuts, bolts, wire, blades, and motors. The current inventory levels and parts list for each type of fan is shown in the table.
  
Fan A sells for $18, Fan B sells for $25, and Fan C sells for $30. Formulate this decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Accepted Answer

The answer of Belsky Manufacturing makes three models of fans,...

Question 7

A producer has three products, A, B, and C, which are composed from many of the same raw materials and subassemblies by the same skilled workforce. Each unit of product A uses 15 units of raw material X, a single purge system subassembly, a case, a power cord, three labor hours in the assembly department, and one labor hour in the finishing department. Each unit of product B uses 10 units of raw material X, five units of raw material Y, two purge system subassemblies, a case, a power cord, five labor hours in the assembly department, and 90 minutes in the finishing department. Each unit of product C uses five units of raw material X, 25 units of raw material Y, two purge system subassemblies, a case, a power cord, seven labor hours in the assembly department, and three labor hours in the finishing department. Labor between the assembly and finishing departments is not transferable, but workers within each department work on any of the three products. There are three full-time (40 hours/week) workers in the assembly department and one full-time and one half-time (20 hours/week) worker in the finishing department. At the start of this week, the company has 300 units of raw material X, 400 units of raw material Y, 60 purge system subassemblies, 40 cases, and 50 power cords in inventory. No additional deliveries of raw materials are expected this week. There is a $90 profit on product A, a $120 profit on product B, and a $150 profit on product C. The operations manager doesn't have any firm orders, but would like to make at least five of each product so he can have the products on the shelf in case a customer wanders in off the street.
Formulate the objective function and all constraints, and clearly identify each constraint by the name of the resource or condition it represents.

Accepted Answer

The answer of A producer has three products, A, B,...

Question 8

A binding constraint has slack but does not have surplus.

Accepted Answer

A binding constraint does not have slack or surplus because it is exactly met in the solution of a linear programming problem, meaning the resources are fully utilized without any excess or shortfall.

Question 9

Scenario D.1
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
-Referring to Scenario D.1, what is an appropriate constraint for this scenario?
A) 4*Eggs + 8*Tomatoes + 14*Chicken ≤ 15
B) 5*Eggs + 1*Tomatoes + 22*Chicken ≥ 20
C) 4*Eggs + 8*Tomatoes + 14*Chicken = 15
D) 15*VitaminA = Eggs + Tomatoes + Chicken

Accepted Answer

The appropriate constraint in this scenario would be ensuring that each four ounce portion has at least 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. The constraint that represents this is 5*Eggs + 1*Tomatoes + 22*Chicken ≥ 20 (for protein), 4*Eggs + 5*Tomatoes + 14*Chicken ≥ 15 (for vitamin A), and 3*Eggs + 14*Tomatoes + 5*Chicken ≥ 10 (for vitamin B). Therefore, the best choice is B.

Question 10

Scenario D.1
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
-Referring to Scenario D.1, what is an appropriate objective function for this scenario?
A) Max Z = .12*Egg + .08*Tomato + .4*Chicken
B) Max Z = 20*Protein + 15*VitaminA + 10*VitaminB
C) Min Z = .12*Egg + .08*Tomato + .4*Chicken
D) Min Z = 20*Protein + 15*VitaminA + 10*VitaminB

Accepted Answer

The objective function should minimize the cost of producing the cat food, which is achieved by minimizing the total cost of the ingredients (eggs, tomatoes, chicken) used in the production.

Question 11

Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 22 units of protein, 15 units of vitamin A, and 8 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 6 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 8 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 8 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 5 cents per ounce, and eggs cost 12 cents per ounce. To make the production process as easy as possible, she would like to make exactly four ounces of cat food from her recipe. Formulate this decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Accepted Answer

The answer of Lisa lives out in the country with...

Question 12

The graphical method is a practical method for solving product mix problems of any size, provided the decision maker has sufficient quantities of graph paper.

Accepted Answer

The statement is false. The graphical method is a practical method for solving product mix problems, but it does not necessarily require large quantities of graph paper. Modern software programs and spreadsheets can also be used for this purpose.

Question 13

The terms slack and surplus both refer to having too much of a resource.

Accepted Answer

Slack refers to the excess of a resource, but surplus specifically refers to the excess of goods or products over what is needed, often used in the context of production or inventory.

Question 14

Only corner points should be considered for the optimal solution to a linear programming problem.

Accepted Answer

This is true. In linear programming, the optimal solution always occurs at one of the corner points (also known as vertices) of the feasible region. This is known as the Corner Point Theorem. Therefore, only the corner points need to be considered when finding the optimal solution.

Question 15

A portfolio manager is trying to balance investments between bonds, stocks and cash. The return on stocks is 12 percent, 9 percent on bonds, and 3 percent on cash. The total portfolio is $1 billion, and he or she must keep 10 percent in cash in accordance with company policy. The fund's prospectus promises that stocks cannot exceed 75 percent of the portfolio, and the ratio of stocks to bonds must equal two. Formulate this investment decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Accepted Answer

The answer of A portfolio manager is trying to balance...

Question 16

NYNEX must schedule round-the-clock coverage for its telephone operators. To keep the number of different shifts down to a manageable level, it has only four different shifts. Operators work eight-hour shifts and can begin work at either midnight, 8 a.m., noon, or 4 p.m. Operators are needed according to the following demand pattern, given in four-hour time blocks.
  
Formulate this scheduling decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Accepted Answer

The answer of NYNEX must schedule round-the-clock coverage for its...

Question 17

Belsky Manufacturing makes three models of fans, identified by the unimaginative names of A, B, and C. The fans are made out of nuts, bolts, wire, blades, and motors. The current inventory levels and parts list for each type of fan is shown in the table.
  
Fan A sells for $18, Fan B sells for $25, and Fan C sells for $30.
Milo Belsky decided to arrive at an optimal production quantity using linear programming. His initial solution was to produce 50 Fan As and 21.4 Fan Cs for a profit of $1,542.86.
Determine what his inventory would be.
Charlie Belsky made an important change to the model and ran the linear programming software again, His solution was to produce 50 Fan As, -150 Fan Bs, and 150 Fan Cs for a profit of $1,650 units. What change did he make to the model and what would the ending inventory be if they were to produce according to this plan? What are the practical implications of this solution?

Accepted Answer

The answer of Belsky Manufacturing makes three models of fans,...

Question 18

Which of the following statements regarding linear programming is not True?
A) A linear programming problem can have more than one optimal solution.
B) Most real-world linear programming problems are solved on a computer.
C) If a binding constraint were relaxed, the optimal solution wouldn't change.
D) A surplus variable is added to a > constraint to convert it to an equality.

Accepted Answer

If a binding constraint were relaxed, the optimal solution may change.

Question 19

Scenario D.1
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
-Referring to Scenario D.1, which of the following statements is best?
A) Making the cat food out of only eggs is optimal
B) Making the cat food out of only eggs is less expensive than making it out of only tomatoes.
C) Making the cat food out of only eggs means that the Vitamin B constraint would not be satisfied.
D) Making the cat food out of only chicken means the Vitamin B constraint would not be satisfied.

Accepted Answer

The answer of Scenario D.1
Lisa lives out in the country...

Question 20

In a linear programming model, the objective function answers the question What is to be maximized?

Accepted Answer

The objective function in a linear programming model is the function that is to be maximized or minimized. It represents the goal or objective of the model.

Quiz 21: Supplement D Linear Programming