Question 1

Identify three examples of resources that are typically constrained in a linear programming problem.

Accepted Answer

The textbook gives m

Question 2

Suppose that the shadow price for assembly time is $5/hour. If all assembly hours were used under the initial LP solution and workers normally make $4/hour but can work overtime for $6/hour, what should management do?

Accepted Answer

A)  do not change available hours for assembly time 
B)  decrease available hours for assembly time 
C)  increase available hours for assembly time 
D)  not enough information 
E)  Either A or C will result in larger profits than B. 
A)  do not change available hours for assembly time 
B)  decrease available hours for assembly time 
C)  increase available hours for assembly time 
D)  not enough information 
E)  Either A or C will result in larger profits than B.

Question 3

Suppose that an iso-profit line is given to be X + Y = 10. Which of the following represents another iso-profit line for the same scenario?

Accepted Answer

A)  X + Y = 15 
B)  X - Y = 10 
C)  Y - X = 10 
D)  2X + Y = 10 
E)  2Y - X = 15 
A)  X + Y = 15 
B)  X - Y = 10 
C)  Y - X = 10 
D)  2X + Y = 10 
E)  2Y - X = 15

Question 4

Suppose that a chemical manufacturer is deciding how to mix two chemicals, A and B. A costs $5/gram and B costs $4/gram if they are ordered above the current supply level. There are currently 40 grams of A and 30 grams of B that must be used in the mix or they will expire. If a customer wants 1 kg of the mix with at least 40% A but no more than 55% A, how many grams of each chemical should be included in the mix?

Accepted Answer

Students should start by using all of th

Question 5

A company has the following inputs and cost structure.
 $$\begin{array} { l l l l } 
\text { Product } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \
\text { Ingredient A } & 4 & 2 & 4 \
\text { Ingredient B } & 2 & 2 & 1 \
\text { Ingredient C } & 1 & 5 & 3 \
\text { Ingredient D } & 6 & 8 & 7 \
\text { Cost per unit } & 0.05 & 0.017 & 0.045
\end{array}$$ They must also use the following minimum quantities.
A 80, B 64, C 90, D 120
The is also a maximum of Z of 100 units.
a) Calculate how many of each product (X, Y, Z) should be produced.
b) How much is the minimized total cost?

Accepted Answer

The answer of A company has the following inputs and...

Question 6

Rienzi Farms grows sugar cane and soybeans on its 500 acres of land. An acre of soybeans brings a $1000 contribution to overhead and profit; an acre of sugar cane has a contribution of $2000. Because of a government program no more than 200 acres may be planted in soybeans. During the planting season 1200 hours of planting time will be available. Each acre of soybeans requires 2 hours, while each acre of sugar cane requires 5 hours. The company seeks maximum contribution (profit) from its planting decision.
a. Algebraically state the decision variables, objective and constraints.
b. Plot the constraints
c. Solve graphically, using the corner-point method.

Accepted Answer

The problem statement is contained in th

Question 7

The ________ is the set of all feasible combinations of the decision variables.

Accepted Answer

The answer of The ________ is the set of all...

Question 8

What combination of x and y will yield the optimum for this problem? Minimize $3x + $15y, subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x, y ≥ 0.

Accepted Answer

A)  x = 2, y = 0 
B)  x = 0, y = 3 
C)  x = 0, y = 0 
D)  x = 1, y = 5 
E)  x = 0, y = 4 
A)  x = 2, y = 0 
B)  x = 0, y = 3 
C)  x = 0, y = 0 
D)  x = 1, y = 5 
E)  x = 0, y = 4

Question 9

An iso-profit line

Accepted Answer

A)  can be used to help solve a profit maximizing linear programming problem. 
B)  is parallel to all other iso-profit lines in the same problem. 
C)  is a line with the same profit at all points. 
D)  all of the above. 
E)  none of the above. 
A)  can be used to help solve a profit maximizing linear programming problem. 
B)  is parallel to all other iso-profit lines in the same problem. 
C)  is a line with the same profit at all points. 
D)  all of the above. 
E)  none of the above.

Question 10

Sensitivity analysis of linear programming solutions can use trial and error or the analytic postoptimality method.

Accepted Answer

A) True 
 B)False

Question 11

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

Accepted Answer

A)  3X ≥ Y 
B)  X ≤ 3Y 
C)  X + Y≥3 
D)  X - 3Y ≥ 0 
E)  3X ≤ Y 
A)  3X ≥ Y 
B)  X ≤ 3Y 
C)  X + Y≥3 
D)  X - 3Y ≥ 0 
E)  3X ≤ Y

Question 12

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a constraint ready for use in problem solving software.

Accepted Answer

The quoted sentence translates into the

Question 13

A financial advisor is about to build an investment portfolio for a client who has $100,000 to invest. The four investments available are A, B, C, and D. Investment A will earn 4% and has a risk of two "points" per $1,000 invested. B earns 6% with 3 risk points; C earns 9% with 7 risk points; and D earns 11% with a risk of 8. The client has put the following conditions on the investments: A is to be no more than one-half of the total invested. A cannot be less than 20% of the total investment. D cannot be less than C. Total risk points must be at or below 1,000.Identify the decision variables of this problem. Write out the objective function and constraints. Do not solve.

Accepted Answer

Maximize 0.04A + 0.06B + 0.09C + 0.11D
S

Question 14

A maximizing linear programming problem with constraints C1, C2, and C3 has been solved. The dual values associated with the problem are C1 = $2, C2 = $0.50, and C3 = $0. Which statement below is false?

Accepted Answer

A)  One more unit of the resource in C1 would add $2 to the objective function value. 
B)  One more unit of the resource in C2 would add one more unit each of X and Y. 
C)  The resource in C3 has not been used up. 
D)  The resources in C1 and in C2, but not in C3, are scarce. 
E)  The resource in C2 must be used up first. 
A)  One more unit of the resource in C1 would add $2 to the objective function value. 
B)  One more unit of the resource in C2 would add one more unit each of X and Y. 
C)  The resource in C3 has not been used up. 
D)  The resources in C1 and in C2, but not in C3, are scarce. 
E)  The resource in C2 must be used up first.

Question 15

The graphical method of solving linear programming can handle only maximizing problems.

Accepted Answer

A) True 
 B)False

Question 16

Suppose that a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be X + 2Y what is the maximum profit the company can earn?

Accepted Answer

A)  $0 
B)  $10 
C)  $15 
D)  $14 
E)  $12 
A)  $0 
B)  $10 
C)  $15 
D)  $14 
E)  $12

Question 17

The feasible region in the diagram below is consistent with which one of the following constraints?

Accepted Answer

A)  8X1 + 4X2 ≤ 160 
B)  8X1 + 4X2 ≥ 160 
C)  4X1 + 8X2 ≤ 160 
D)  8X1 - 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160 
A)  8X1 + 4X2 ≤ 160 
B)  8X1 + 4X2 ≥ 160 
C)  4X1 + 8X2 ≤ 160 
D)  8X1 - 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160

Question 18

A manager must decide on the mix of products to produce for the coming week. Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute for packing. Product B requires two minutes per unit for molding, four minutes for painting, and three minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing. Both products have contributions of $1.50 per unit. Answer the following questions; base your work on the solution panel provided.
 $$\begin{array} { | l | r | r | r | r | r | } 
\hline & \mathrm { A } & \mathrm { B } & & \text { RHS } & \text { Dual } \
\hline \text { Maximize } & 1.5 & 1.5 & & & \
\hline \text { Molding } & 3 & 2 . & \square & 600 & 0.375 \
\hline \text { Painting } & 2 & 4 &\square & 600 & 0.1875 \
\hline \text { Packing } & 1 . & 3 & \square& 420 & 0 . \
\hline \text { Solution --- } & 150 & 75 & & 337.5 & \
\hline
\end{array}$$ a. What combination of A and B will maximize contribution?
b. What is the maximum possible contribution?
c. Are any resources not fully used up? Explain.

Accepted Answer

Maximum contribution occurs at A = 150,

Question 19

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

Accepted Answer

A) True 
 B)False

Question 20

The Queen City Nursery manufactures bags of potting soil from compost and topsoil. Each cubic foot of compost costs 12 cents and contains 4 pounds of sand, 3 pounds of clay, and 5 pounds of humus. Each cubic foot of topsoil costs 20 cents and contains 3 pounds of sand, 6 pounds of clay, and 12 pounds of humus. Each bag of potting soil must contain at least 12 pounds of sand, 12 pounds of clay, and 10 pounds of humus. Explain how this problem meets the conditions of a linear programming problem. Plot the constraints and identify the feasible region. Graphically or with corner points find the best combination of compost and topsoil that meets the stated conditions at the lowest cost per bag. Identify the lowest cost possible.

Accepted Answer

The problem formulation appears in the s

Exam 19: Linear Programming

Identify three examples of resources that are typically constrained in a linear programming problem.

Suppose that the shadow price for assembly time is $5/hour. If all assembly hours were used under the initial LP solution and workers normally make $4/hour but can work overtime for $6/hour, what should management do?

Suppose that an iso-profit line is given to be X + Y = 10. Which of the following represents another iso-profit line for the same scenario?

The ________ is the set of all feasible combinations of the decision variables.

What combination of x and y will yield the optimum for this problem? Minimize $3x + $15y, subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x, y ≥ 0.

An iso-profit line

Sensitivity analysis of linear programming solutions can use trial and error or the analytic postoptimality method.

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a constraint ready for use in problem solving software.

A maximizing linear programming problem with constraints C1, C2, and C3 has been solved. The dual values associated with the problem are C1 = $2, C2 = $0.50, and C3 = $0. Which statement below is false?

The graphical method of solving linear programming can handle only maximizing problems.

Suppose that a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be X + 2Y what is the maximum profit the company can earn?

The feasible region in the diagram below is consistent with which one of the following constraints?

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

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