Question 1

In order for a linear programming problem to have multiple solutions, the solution must exist

Accepted Answer

A) at the intersection of the non-negativity constraints. 
B) on a non-redundant constraint parallel to the objective function. 
C) at the intersection of the objective function and a constraint. 
D) at the intersection of three or more constraints. 
A) at the intersection of the non-negativity constraints. 
B) on a non-redundant constraint parallel to the objective function. 
C) at the intersection of the objective function and a constraint. 
D) at the intersection of three or more constraints.

Question 2

What is the increase in the objective value if 2 units of additive are added?

Accepted Answer

A) 0 
B) 4 
C) 12 
D) 16 
A) 0 
B) 4 
C) 12 
D) 16

Question 3

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y)cannot be the optimal solution?

Accepted Answer

A) (0, 0) 
B) (0, 100) 
C) (65, 65) 
D) (100, 0) 
A) (0, 0) 
B) (0, 100) 
C) (65, 65) 
D) (100, 0)

Question 4

Which of the following is not acceptable as a constraint in a linear programming problem (maximization)? Constraint 1 X + XY + Y ≥ 12
Constraint 2 X - 2Y ≤ 20
Constraint 3 X + 3Y = 48
Constraint 4 X + Y + Z ≤ 150

Accepted Answer

A) Constraint 1 
B) Constraint 2 
C) Constraint 3 
D) Constraint 4 
A) Constraint 1 
B) Constraint 2 
C) Constraint 3 
D) Constraint 4

Question 5

Which of the following is not a property of linear programs?

Accepted Answer

A) one objective function 
B) at least two separate feasible regions 
C) alternative courses of action 
D) one or more constraints 
A) one objective function 
B) at least two separate feasible regions 
C) alternative courses of action 
D) one or more constraints

Question 6

If one changes the contribution rates in the objective function of an LP

Accepted Answer

A) the feasible region will change. 
B) the slope of the isoprofit or isocost line will change. 
C) the optimal solution to the LP is sure to no longer be optimal. 
D) the problem will no longer be linear. 
A) the feasible region will change. 
B) the slope of the isoprofit or isocost line will change. 
C) the optimal solution to the LP is sure to no longer be optimal. 
D) the problem will no longer be linear.

Question 7

Which of the following functions is not linear?

Accepted Answer

A) 5X + 3Z 
B) 3X + 4Y + Z - 3 
C) 2X + 5YZ 
D) Z 
A) 5X + 3Z 
B) 3X + 4Y + Z - 3 
C) 2X + 5YZ 
D) Z

Question 8

A furniture company is producing two types of furniture.Product A requires 8 board feet of wood and 2 lbs of wicker.Product B requires 6 board feet of wood and 6 lbs of wicker.There are 2000 board feet of wood available for product and 1000 lbs of wicker.Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit.Which of these is an appropriate constraint for Wood?

Accepted Answer

A) 30A + 40B ≤ 2000 
B) 8A + 6B ≤ 2000 
C) 8A + 2B ≤ 2000 
D) 2A + 6B ≤ 2000 
A) 30A + 40B ≤ 2000 
B) 8A + 6B ≤ 2000 
C) 8A + 2B ≤ 2000 
D) 2A + 6B ≤ 2000

Question 9

One basic assumption of linear programming is proportionality.Explain its need.

Accepted Answer

Rates of consumption exist and are const

Question 10

In a maximization problem, when one or more of the solution variables and the profit can be made infinitely large without violating any constraints, the linear program has

Accepted Answer

A) an infeasible solution. 
B) an unbounded solution. 
C) a redundant constraint. 
D) alternate optimal solutions. 
A) an infeasible solution. 
B) an unbounded solution. 
C) a redundant constraint. 
D) alternate optimal solutions.

Question 11

Compare the shadow price to the dual price.

Accepted Answer

For maximization problems, the

Question 12

Consider the following linear program: Maximize 30X + 10Y
Subject to: 3X + Y ≤ 300
X + Y ≤ 200
X ≤ 100
Y ≥ 50
X,Y ≥ 0
What is the optimal solution?

Accepted Answer

A) $3,000 
B) $3,200 
C) $3,400 
D) $3,600 
A) $3,000 
B) $3,200 
C) $3,400 
D) $3,600

Question 13

The simultaneous equation method is

Accepted Answer

A) an alternative to the corner point method. 
B) useful only in minimization methods. 
C) an algebraic means for solving the intersection of two or more constraint equations. 
D) useful only when more than two product variables exist in a product mix problem. 
A) an alternative to the corner point method. 
B) useful only in minimization methods. 
C) an algebraic means for solving the intersection of two or more constraint equations. 
D) useful only when more than two product variables exist in a product mix problem.

Question 14

Consider the following linear programming problem: 
Maximize 4X + 10Y
Subject to: 3X + 4Y ≤ 480
4X + 2Y ≤ 360
All variable ≥ 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).What is the maximum possible value for the objective function?

Accepted Answer

A) 1032 
B) 1200 
C) 360 
D) 1600 
A) 1032 
B) 1200 
C) 360 
D) 1600

Question 15

The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed of chicken and liver-flavored biscuits)that meets certain nutritional requirements.The liver-flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chicken-flavored ones contain 1 unit of nutrient A and 4 units of nutrient B.According to federal requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package of the new biscuit mix.In addition, the company has decided that there can be no more than 15 liver-flavored biscuits in a package.If it costs 1 cent to make a liver-flavored biscuit and 2 cents to make a chicken-flavored one, what is the optimal product mix for a package of the biscuits in order to minimize the firm's cost?
(a)Formulate this as a linear programming problem.
(b)Find the optimal solution for this problem graphically.
(c)Are any constraints redundant? If so, which one or ones?
(d)What is the total cost of a package of dog biscuits using the optimal mix?

Accepted Answer

(a)Let X₁ = number of liver-flavored bisc

Question 16

Sensitivity analysis may also be called

Accepted Answer

A) postoptimality analysis. 
B) nonparametric programming. 
C) preoptimality analysis. 
D) redundancy testing 
A) postoptimality analysis. 
B) nonparametric programming. 
C) preoptimality analysis. 
D) redundancy testing

Question 17

In a linear program, the constraints must be linear, but the objective function may be nonlinear.

Accepted Answer

A) True 
 B)False

Question 18

Define dual price.

Accepted Answer

The dual price for a constrain

Question 19

Determine where the following two constraints intersect.
2X - 4Y = 800
−X + 6Y ≥ -200

Accepted Answer

The answer of Determine where the following two constraints intersect.
2X...

Question 20

One basic assumption of linear programming is non-negativity.What does this imply and how reasonable is this assumption?

Accepted Answer

This assumption states that only positiv

Exam 7: Linear Programming Models: Graphical and Computer Methods

In order for a linear programming problem to have multiple solutions, the solution must exist

What is the increase in the objective value if 2 units of additive are added?

Consider the following constraints from a linear programming problem: 2X + Y ≤ 200 X + 2Y ≤ 200 X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y)cannot be the optimal solution?

Which of the following is not acceptable as a constraint in a linear programming problem (maximization)? Constraint 1 X + XY + Y ≥ 12 Constraint 2 X - 2Y ≤ 20 Constraint 3 X + 3Y = 48 Constraint 4 X + Y + Z ≤ 150

Which of the following is not a property of linear programs?

If one changes the contribution rates in the objective function of an LP

Which of the following functions is not linear?

One basic assumption of linear programming is proportionality.Explain its need.

In a maximization problem, when one or more of the solution variables and the profit can be made infinitely large without violating any constraints, the linear program has

Compare the shadow price to the dual price.

Consider the following linear program: Maximize 30X + 10Y Subject to: 3X + Y ≤ 300 X + Y ≤ 200 X ≤ 100 Y ≥ 50 X,Y ≥ 0 What is the optimal solution?

The simultaneous equation method is

Consider the following linear programming problem: Maximize 4X + 10Y Subject to: 3X + 4Y ≤ 480 4X + 2Y ≤ 360 All variable ≥ 0 The feasible corner points are (48,84), (0,120), (0,0), (90,0).What is the maximum possible value for the objective function?

Sensitivity analysis may also be called

In a linear program, the constraints must be linear, but the objective function may be nonlinear.

Define dual price.

Determine where the following two constraints intersect. 2X - 4Y = 800 −X + 6Y ≥ -200

One basic assumption of linear programming is non-negativity.What does this imply and how reasonable is this assumption?

Introduction to Quantitative Analysis

Probability Concepts and Applications

Decision Analysis

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Forecasting

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Integer Programming, Goal Programming, and Nonlinear Programming

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Dynamic Programming

Decision Theory and the Normal Distribution

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Mathematical Tools: Determinants and Matrices

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Linear Programming: The Simplex Method

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