Question 1

In sensitivity analysis,a zero shadow price (or dual value)for a resource ordinarily means that the resource has not been used up.

Accepted Answer

A) True 
 B)False

Question 2

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), (33.3333,8.3333),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), (33.3333,8.3333),and (100,0). 
E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

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) the profit contribution necessary for that item to be included in the optimal solution 
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) the profit contribution necessary for that item to be included in the optimal solution

Question 4

The requirements of linear programming problems include an objective function,the presence of constraints,objective and constraints expressed in linear equalities or inequalities,and ________.

Accepted Answer

alternativ

Question 5

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,at least 12 pounds of clay,and at least 10 pounds of humus.Formulate the problem as a linear program.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

Let C = cubic feet of compost used per b

Question 6

What is linear programming?

Accepted Answer

Linear programming is a mathem

Question 7

For the constraints given below,which point is in the feasible region of this maximization problem? (1)14x + 6y ≤ 42 (2)x - y ≤ 3 (3)x,y ≥ 0

Accepted Answer

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

Question 8

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 percent and has a risk of two "points" per $1,000 invested.B earns 6 percent with 3 risk points;C earns 9 percent with 7 risk points;and D earns 11 percent 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 percent of the total investment.D cannot be less than C.Total risk points must be at or below 1,000.
Let A be the amount invested in investment A,and define B,C,and D similarly.
Formulate the linear programming model.

Accepted Answer

Maximize return = 0.04A + 0.06B + 0.09C

Question 9

What is the feasible region in a linear programming problem?

Accepted Answer

The feasible region

Question 10

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 11

________ are restrictions that limit the degree to which a manager can pursue an objective.

Accepted Answer

The answer of ________ are restrictions that limit the degree...

Question 12

Which of the following combinations of constraints has no feasible region?

Accepted Answer

A) X + Y ≥ 15 and X - Y ≤ 10 
B) X + Y ≥ 5 and X ≥ 10 
C) X ≥ 10 and Y ≥ 20 
D) X + Y ≥ 100 and X + Y ≤ 50 
E) X ≤ -5 
A) X + Y ≥ 15 and X - Y ≤ 10 
B) X + Y ≥ 5 and X ≥ 10 
C) X ≥ 10 and Y ≥ 20 
D) X + Y ≥ 100 and X + Y ≤ 50 
E) X ≤ -5

Question 13

A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R,S,and T." Formulate this as a linear programming constraint.

Accepted Answer

Q ≥ R + S

Question 14

In the graphical solution to a linear program,the region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Accepted Answer

A) True 
 B)False

Question 15

Two methods of solving linear programming problems by hand include the corner-point method and the ________.

Accepted Answer

iso-profit

Question 16

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

Accepted Answer

The iso-profit line is moved up in a max

Question 17

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.
   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,B

Question 18

Sensitivity analysis can be applied to linear programming solutions by either (1)trial and error or (2)the analytic postoptimality method.

Accepted Answer

A) True 
 B)False

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

A linear programming problem contains a restriction that reads "the quantity of S must be no more than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

Accepted Answer

S ≤ .25 T

Exam 23: Linear Programming Models

In sensitivity analysis,a zero shadow price (or dual value)for a resource ordinarily means that the resource has not been used up.

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?

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

The requirements of linear programming problems include an objective function,the presence of constraints,objective and constraints expressed in linear equalities or inequalities,and ________.

What is linear programming?

For the constraints given below,which point is in the feasible region of this maximization problem? (1)14x + 6y ≤ 42 (2)x - y ≤ 3 (3)x,y ≥ 0

What is the feasible region in a linear programming problem?

________ are restrictions that limit the degree to which a manager can pursue an objective.

Which of the following combinations of constraints has no feasible region?

A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R,S,and T." Formulate this as a linear programming constraint.

In the graphical solution to a linear program,the region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Two methods of solving linear programming problems by hand include the corner-point method and the ________.

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

Sensitivity analysis can be applied to linear programming solutions by either (1)trial and error or (2)the analytic postoptimality method.

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

A linear programming problem contains a restriction that reads "the quantity of S must be no more than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

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