Question 1

The region that satisfies all of the constraints in graphical linear programming is called the region of optimality.

Accepted Answer

A) True 
 B)False

Question 2

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 3

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) the resource is very costly. 
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) the resource is very costly.

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

Tom is a habitual shopper at garage sales.Last Saturday he stopped at one where there were several types of used building materials for sale.At the low prices being asked,Tom knew that he could resell the items in another town for a substantial gain.Four things stood in his way: he could only make one round trip to resell the goods;his pickup truck bed would hold only 1000 pounds;the pickup truck bed could hold at most 70 cubic feet of merchandise;and he had only $200 cash with him.He wants to load his truck with the mix of materials that will yield the greatest profit when he resells them.
   State the decision variables (give them labels).State the objective function.Formulate the constraints of this problem.Do not solve,but speculate on what might be a good solution for Tom.You must supply a set of quantities for the decision variables.Provide a sentence or two of support for your choice.

Accepted Answer

Student responses must be feasible,but n

Question 6

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.

Question 7

The difference between minimization and maximization problems is that

Accepted Answer

A) minimization problems cannot be solved with the corner-point method. 
B) maximization problems often have unbounded regions. 
C) minimization problems often have unbounded regions. 
D) minimization problems cannot have shadow prices. 
E) None of the above are true. 
A) minimization problems cannot be solved with the corner-point method. 
B) maximization problems often have unbounded regions. 
C) minimization problems often have unbounded regions. 
D) minimization problems cannot have shadow prices. 
E) None of the above are true.

Question 8

What is the simplex method?

Accepted Answer

The simplex method i

Question 9

The objective of a linear programming problem is to maximize 1.50A + 1.50B,subject to 3A + 2B ≤ 600,2A + 4B ≤ 600,and 1A + 3B ≤ 420.
a.Plot the constraints on the grid below
b.Identify the feasible region and its corner points.Show your work.
c.What is the optimal product mix for this problem?

Accepted Answer

The objective of the problem is to maxim

Question 10

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 11

What is the usefulness of a shadow price (or dual value)?

Accepted Answer

Shadow prices and dual values are found

Question 12

Which of the following is not a requirement of a linear programming problem?

Accepted Answer

A) an objective function,expressed in terms of linear equations 
B) constraint equations,expressed as linear equations 
C) an objective function,to be maximized or minimized 
D) alternative courses of action 
E) for each decision variable,there must be one constraint or resource limit 
A) an objective function,expressed in terms of linear equations 
B) constraint equations,expressed as linear equations 
C) an objective function,to be maximized or minimized 
D) alternative courses of action 
E) for each decision variable,there must be one constraint or resource limit

Question 13

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) maximize $20Y + $50Z. 
A) maximize $40Y = $25Z. 
B) maximize $40Y + $25Z. 
C) maximize $30Y + $20Z. 
D) maximize 0.25Y + 0.20Z. 
E) maximize $20Y + $50Z.

Question 14

Lost Maples Winery makes three varieties of contemporary Texas Hill Country wines: Austin Formation (a fine red),Ste.Genevieve (a table white),and Los Alamos (a hearty pink Zinfandel).The raw materials,labour,and contribution per case of each of these wines is summarized below.
   The winery has 2800 bushels of Variety A grapes,2040 bushels of Variety B grapes,800 pounds of sugar,and 1060 man-hours of labour available during the next week.The firm operates to achieve maximum contribution.Refer to the POM for Windows panels showing the solution to this problem.   Answer the following questions.
a.For maximum contribution,how much of each wine should be produced?
b.How much contribution will be made by selling the output?
c.Is there any sugar left over? If so,how much? If not,what is its shadow price (dual value)? Explain what this value means to Lost Maples' management.
d.Interpret the meaning of the lower bound to Labour in the Ranging analysis.That is,explain how the solution would change if the amount of labour fell below that lower value.
e.Interpret the meaning of the upper bound to Los Alamos wine in the Ranging analysis.

Accepted Answer

(a)183 1/3 cases of Austin Formation,510

Question 15

What combination of x and y will yield the optimum for this problem? Maximize $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) none of the above 
A) x = 2,y = 0 
B) x = 0,y = 3 
C) x = 0,y = 0 
D) x = 1,y = 5 
E) none of the above

Question 16

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 17

In linear programming,if there are three constraints,each representing a resource that can be used up,the optimal solution must use up all of each of the three resources.

Accepted Answer

A) True 
 B)False

Question 18

In a linear programming problem,what is the relationship between the constraints and the feasible region? Explain with reference to a problem with two variables.

Accepted Answer

Each constraint appears on a graph as an

Question 19

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 20

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

Accepted Answer

A) True 
 B)False

Exam 22: Linear Programming

The region that satisfies all of the constraints in graphical linear programming is called the region of optimality.

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

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?

The difference between minimization and maximization problems is that

What is the simplex method?

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?

What is the usefulness of a shadow price (or dual value)?

Which of the following is not a requirement of a linear programming problem?

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

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

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

In linear programming,if there are three constraints,each representing a resource that can be used up,the optimal solution must use up all of each of the three resources.

In a linear programming problem,what is the relationship between the constraints and the feasible region? Explain with reference to a problem with two variables.

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

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

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