Question 1

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 maximization problem until it no longer intersects with any constraint equation.The last point in the feasible region that the line touches is the optimal solution.

Question 2

Suppose that a constraint is given by X + Y ≤ 10.If another constraint is given to be 3X + 2Y ≥ 15,and if X and Y are restricted to be nonnegative,determine the corners of the feasible solution.If the profit from X is 5 and the profit from Y is 10,determine the combination of X and Y that will yield maximum profit.

Accepted Answer

Corners are (10,0), (5,0), (0,7.5),and (0,10).Maximum profit is at the corner (0,10),which yields $100 of profit.

Question 3

In linear programming,statements such as "the blend must consist of at least 10% of ingredient A,at least 30% of ingredient B,and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

Accepted Answer

A) True 
 B)False  True

Question 4

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 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.
   Formulate this problem as a linear program.

Accepted Answer

Let S be the number of studs purchased
L

Question 6

________ 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 7

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100;4X + 6Y ≤ 120;6X + 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 8

________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

Accepted Answer

Sensitivit

Question 9

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 10

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 11

What combination of a and b will yield the optimum for this problem? Maximize $6a + $15b,subject to (1)4a + 2b ≤ 12 and (2)5a + 2b ≤ 20 and (3)x,y ≥ 0.

Accepted Answer

A) a = 0,b = 0 
B) a = 3,b = 3 
C) a = 0,b = 6 
D) a = 6,b = 0 
E) a = 0,b = 10 
A) a = 0,b = 0 
B) a = 3,b = 3 
C) a = 0,b = 6 
D) a = 6,b = 0 
E) a = 0,b = 10

Question 12

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

Accepted Answer

iso-profit

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

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 15

Phil Bert's Nuthouse is preparing a new product,a blend of mixed nuts.The product must be at most 50 percent peanuts,must have more almonds than cashews,and must be at least 10 percent pecans.The blend will be sold in one-pound bags.Phil's goal is to mix the nuts in such a manner that all conditions are satisfied and the cost per bag is minimized.Peanuts cost $1 per pound.Cashews cost $3 per pound.Almonds cost $5 per pound and pecans cost $6 per pound.Formulate this problem as a linear program.

Accepted Answer

Call the variables PN,AL,CA,and PC
Minim

Question 16

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

Accepted Answer

A) S / (T + U)≥ 4 
B) S - .25T -.25U ≥ 0 
C) 4S ≤ T + U 
D) S ≥ 4T / 4U 
E) S ≥ .25T + S ≥ .25U 
A) S / (T + U)≥ 4 
B) S - .25T -.25U ≥ 0 
C) 4S ≤ T + U 
D) S ≥ 4T / 4U 
E) S ≥ .25T + S ≥ .25U

Question 17

Which of the following is an algorithm for solving linear programming problems of all sizes?

Accepted Answer

A) duplex method 
B) multiplex method 
C) shadow price method 
D) simplex method 
E) decision tree method 
A) duplex method 
B) multiplex method 
C) shadow price method 
D) simplex method 
E) decision tree method

Question 18

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

Question 19

In terms of linear programming,the fact that the solution is infeasible implies that the "profit" can increase without limit.

Accepted Answer

A) True 
 B)False

Question 20

________ is a mathematical technique designed to help operations managers plan and make decisions necessary to allocate resources.

Accepted Answer

The answer of ________ is a mathematical technique designed to...

Exam 23: Linear Programming

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

In linear programming,statements such as "the blend must consist of at least 10% of ingredient A,at least 30% of ingredient B,and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

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?

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

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100;4X + 6Y ≤ 120;6X + 3Y ≥ 90. What is the largest quantity of X that can be made without violating any of these constraints?

________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

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

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

What combination of a and b will yield the optimum for this problem? Maximize $6a + $15b,subject to (1)4a + 2b ≤ 12 and (2)5a + 2b ≤ 20 and (3)x,y ≥ 0.

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

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

Which of the following is an algorithm for solving linear programming problems of all sizes?

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.

In terms of linear programming,the fact that the solution is infeasible implies that the "profit" can increase without limit.

________ is a mathematical technique designed to help operations managers plan and make decisions necessary to allocate resources.

Operations and Productivity

Operations Strategy in a Global Environment

Project Management

Forecasting

Design of Goods and Services

Managing Quality

Process Strategy

Location Strategies

Layout Strategies

Human Resources,job Design,and Work Measurement

Supply Chain Management

Inventory Management

Aggregate Planning and Sop

Material Requirements Planning Mrpand Erp

Short-Term Scheduling

Jit,tps,and Lean Operations

Maintenance and Reliability

Sustainability in the Supply Chain

Statistical Process Control

Capacity and Constraint Management

Supply Chain Management Analytics

Decision-Making Tools

Transportation Models

Waiting-Line Models

Learning Curves

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