Question 1

The region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Accepted Answer

A) True 
 B)False  False

Question 2

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 the A and B supplies on hand. This totals 70grams and means that 930 grams will need to be ordered. A must have between 400 and 550 grams while B will be 1000-A grams. Removing the already assigned supplies gives that
A (ordered) between 360 and 510
B(ordered) = 930-A => A+B=930
Students should then recognize that the corner points lie where A=360 (ordered), B=570 (ordered) and A = 510 (ordered) and B = 420 (ordered). Using the corner-point approach, the total cost will be minimized at one of these two locations.
TC(A=360 ordered) = 360*5+570*4 = $4080
TC(A=510 ordered) = 510*5+420*4 = $4230
Thus the manufacturer should order 360 grams of A and 570 grams of B. Mixing these ordered supplies with the on hand inventory (treated as being free since it will expire) would give a mix of 400 grams of A and 600 grams of B.

Question 3

A shadow price (or dual value) reflects which of the following in a maximization problem?

Accepted Answer

A)  the marginal gain in the objective realized by subtracting one unit of a resource 
B)  the market price that must be paid to obtain additional resources 
C)  the increase in profit that would accompany one added unit of a scarce resource 
D)  the reduction in cost that would accompany a one unit decrease in the resource 
E)  none of the above 
A)  the marginal gain in the objective realized by subtracting one unit of a resource 
B)  the market price that must be paid to obtain additional resources 
C)  the increase in profit that would accompany one added unit of a scarce resource 
D)  the reduction in cost that would accompany a one unit decrease in the resource 
E)  none of the above C

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

A maximizing linear programming problem has two constraints: 2X + 4Y < 100 and 3X + 10Y < 210, in addition to constraints stating that both X and Y must be nonnegative. The corner points of the feasible region of this problem are

Accepted Answer

A)  (0, 0), (50, 0), (0, 21), and (20, 15) 
B)  (0, 0), (70, 0), (25, 0), and (15, 20) 
C)  (20, 15) 
D)  (0, 0), (0, 100), and (210, 0) 
E)  none of the above 
A)  (0, 0), (50, 0), (0, 21), and (20, 15) 
B)  (0, 0), (70, 0), (25, 0), and (15, 20) 
C)  (20, 15) 
D)  (0, 0), (0, 100), and (210, 0) 
E)  none of the above

Question 6

A linear programming problem has three constraints: 2X + 10Y ≤ 1004X + 6Y ≤ 1206X + 3Y ≤ 90
What is the largest quantity of X that can be made without violating any of these constraints?

Accepted Answer

A)  50 
B)  30 
C)  20 
D)  15 
E)  10 
A)  50 
B)  30 
C)  20 
D)  15 
E)  10

Question 7

Explain how to use the iso-profit line in a graphical maximization problem.

Accepted Answer

The iso-profit line is moved up in a max

Question 8

In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that

Accepted Answer

A)  the resource is scarce 
B)  the resource constraint was redundant 
C)  the resource has not been used up 
D)  something is wrong with the problem formulation 
E)  none of the above 
A)  the resource is scarce 
B)  the resource constraint was redundant 
C)  the resource has not been used up 
D)  something is wrong with the problem formulation 
E)  none of the above

Question 9

What are the requirements of all linear programming problems?

Accepted Answer

Linear programming problems require (1)

Question 10

For the two constraints given below, which point is in the feasible region of this minimization problem? (1) 14x + 6y > 42 $\quad $$\quad $(2) x - y > 3

Accepted Answer

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

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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.
a. Algebraically state the objective and constraints of this problem.
b. Plot the constraints on the grid below and identify the feasible region.

Accepted Answer

The objective of the problem i

Question 13

Suppose that a constraint for assembly time has a shadow price of $50/hour for 15 hours in either direction and that all available assembly time is currently used (would require overtime to do more). If the salary of workers is $30 and they receive 50% extra pay for overtime what should management do?

Accepted Answer

Reducing assembly time would save $30/ho

Question 14

Constraints are needed to solve linear programming problems by hand, but not by computer.

Accepted Answer

A) True 
 B)False

Question 15

A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal were to maximize profit, the appropriate objective function would be

Accepted Answer

A)  maximize $40Y = $25Z 
B)  maximize $40Y + $25Z 
C)  maximize $30Y + $20Z 
D)  maximize 0.25Y + 0.20Z 
E)  none of the above 
A)  maximize $40Y = $25Z 
B)  maximize $40Y + $25Z 
C)  maximize $30Y + $20Z 
D)  maximize 0.25Y + 0.20Z 
E)  none of the above

Question 16

The optimal solution to a linear programming problem is within the feasible region.

Accepted Answer

A) True 
 B)False

Question 17

Suppose that a maximization LP problem has corners of (0,0), (5,0), and (0,5). How many possible combinations of X and Y will yield the maximum profit if profit is given to be 5X+5Y?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  5 
E)  Infinite 
A)  0 
B)  1 
C)  2 
D)  5 
E)  Infinite

Question 18

A synonym for shadow price is __________.

Accepted Answer

The answer of A synonym for shadow price is __________....

Question 19

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

Accepted Answer

A)  area of optimal solutions 
B)  area of feasible solutions 
C)  profit maximization space 
D)  region of optimality 
E)  region of non-negativity 
A)  area of optimal solutions 
B)  area of feasible solutions 
C)  profit maximization space 
D)  region of optimality 
E)  region of non-negativity

Question 20

A linear programming problem has two constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

Accepted Answer

A)  There are four corner points including (50, 0) and (0, 12.5). 
B)  The two corner points are (0, 0) and (50, 12.5). 
C)  The graphical origin (0, 0) is in the feasible region. 
D)  The feasible region is triangular in shape, bounded by (50, 0), (33-1/3, 8-1/3), and (100, 0). 
E)  The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. 
A)  There are four corner points including (50, 0) and (0, 12.5). 
B)  The two corner points are (0, 0) and (50, 12.5). 
C)  The graphical origin (0, 0) is in the feasible region. 
D)  The feasible region is triangular in shape, bounded by (50, 0), (33-1/3, 8-1/3), and (100, 0). 
E)  The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

Exam 22: Linear Programming

The region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

A shadow price (or dual value) reflects which of the following in a maximization problem?

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

A maximizing linear programming problem has two constraints: 2X + 4Y < 100 and 3X + 10Y < 210, in addition to constraints stating that both X and Y must be nonnegative. The corner points of the feasible region of this problem are

A linear programming problem has three constraints: 2X + 10Y ≤ 1004X + 6Y ≤ 1206X + 3Y ≤ 90 What is the largest quantity of X that can be made without violating any of these constraints?

Explain how to use the iso-profit line in a graphical maximization problem.

In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that

What are the requirements of all linear programming problems?

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

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

Constraints are needed to solve linear programming problems by hand, but not by computer.

A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal were to maximize profit, the appropriate objective function would be

The optimal solution to a linear programming problem is within the feasible region.

Suppose that a maximization LP problem has corners of (0,0), (5,0), and (0,5). How many possible combinations of X and Y will yield the maximum profit if profit is given to be 5X+5Y?

A synonym for shadow price is __________.

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

A linear programming problem has two constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

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For the two constraints given below, which point is in the feasible region of this minimization problem? (1) 14x + 6y > 42 $\quad$ $\quad$ (2) x - y > 3