Question 1

Which of the following sets of constraints results in an unbounded maximization problem?

Accepted Answer

A)  X + Y ≥ 100 and X + Y ≤ 50 
B)  X + Y ≥ 15 and X - Y ≤ 10 
C)  X + Y ≤ 10 and X ≥ 5 
D)  X ≤ 10 and Y ≤ 20 
E)  All of these have a bounded maximum. 
A)  X + Y ≥ 100 and X + Y ≤ 50 
B)  X + Y ≥ 15 and X - Y ≤ 10 
C)  X + Y ≤ 10 and X ≥ 5 
D)  X ≤ 10 and Y ≤ 20 
E)  All of these have a bounded maximum.

Question 2

The feasible region in the diagram below is consistent with which one of the following constraints?

Accepted Answer

A)  8X1 + 4X2 ≥ 160 
B)  4X1 + 8X2 ≤ 160 
C)  8X1 - 4X2 ≤ 160 
D)  8X1 + 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160 
A)  8X1 + 4X2 ≥ 160 
B)  4X1 + 8X2 ≤ 160 
C)  8X1 - 4X2 ≤ 160 
D)  8X1 + 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160

Question 3

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

Accepted Answer

A) True 
 B)False

Question 4

The corner-point solution method requires:

Accepted Answer

A)  identifying the corner of the feasible region that has the sharpest angle. 
B)  moving the iso-profit line to the highest level that still touches some part of the feasible region. 
C)  moving the iso-profit line to the lowest level that still touches some part of the feasible region. 
D)  finding the coordinates at each corner of the feasible solution space. 
E)  none of these 
A)  identifying the corner of the feasible region that has the sharpest angle. 
B)  moving the iso-profit line to the highest level that still touches some part of the feasible region. 
C)  moving the iso-profit line to the lowest level that still touches some part of the feasible region. 
D)  finding the coordinates at each corner of the feasible solution space. 
E)  none of these

Question 5

________ variables allow us to introduce "yes-or-no" decisions into our linear programs and to introduce special logical conditions.

Accepted Answer

The answer of ________ variables allow us to introduce "yes-or-no"...

Question 6

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 7

What combination of x and y will yield the optimum for this problem? Minimize $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)  x = 0, y = 5 
A)  x = 2, y = 0 
B)  x = 0, y = 3 
C)  x = 0, y = 0 
D)  x = 1, y = 5 
E)  x = 0, y = 5

Question 8

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 9

Data Corp. is considering which of 4 different projects to undertake in order to maximize its net present value (NPV). Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1, 2, 3, 4. The NPV and required capital (in millions) for each project are listed below.   Which of the following represents the constraint stating that project 2 can be undertaken only if project 3 is undertaken?

Accepted Answer

A)  X2 + X3 ≤ 1 
B)  X2 - X3 ≤ 0 
C)  X3 - X2 ≤ 0 
D)  X2 - X3 ≤ 1 
E)  X3 - X2 ≤ 1 
A)  X2 + X3 ≤ 1 
B)  X2 - X3 ≤ 0 
C)  X3 - X2 ≤ 0 
D)  X2 - X3 ≤ 1 
E)  X3 - X2 ≤ 1

Question 10

Which of the following correctly describes all iso-profit lines for an LP maximization problem?

Accepted Answer

A)  They all pass through the origin 
B)  They are all parallel. 
C)  They all pass through the point of maximum profit. 
D)  Each line passes through at least 2 corners. 
E)  all of these 
A)  They all pass through the origin 
B)  They are all parallel. 
C)  They all pass through the point of maximum profit. 
D)  Each line passes through at least 2 corners. 
E)  all of these

Question 11

If we wish to ensure that decision variable values in a linear program are integers rather than fractions, the generally accepted practice is to round the solutions to the nearest integer values.

Accepted Answer

A) True 
 B)False

Question 12

What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 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)  x = 0, y = 4 
A)  x = 2, y = 0 
B)  x = 0, y = 3 
C)  x = 0, y = 0 
D)  x = 1, y = 5 
E)  x = 0, y = 4

Question 13

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 not in the feasible region. 
D)  The feasible region includes all points that satisfy one constraint, the other, or both. 
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 not in the feasible region. 
D)  The feasible region includes all points that satisfy one constraint, the other, or both. 
E)  The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

Question 14

The diet problem is known in agricultural applications as the:

Accepted Answer

A)  fertilizer problem. 
B)  feed-mix problem. 
C)  crop-rotation problem. 
D)  egg-choice problem. 
E)  genetic-transformation problem. 
A)  fertilizer problem. 
B)  feed-mix problem. 
C)  crop-rotation problem. 
D)  egg-choice problem. 
E)  genetic-transformation problem.

Question 15

A linear programming problem has three constraints, plus nonnegativity constraints on X and Y. The constraints are: 2X + 10Y ≤ 100; 4X + 6Y ≤ 120; 3X + 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 16

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,

Question 17

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 18

Identify three examples of resources that are typically constrained in a linear programming problem.

Accepted Answer

The textbook gives m

Question 19

Suppose that the shadow price for assembly time is $5/hour. The allowable increase for the assembly time constraint is 40 hours, and the allowable decrease is 30 hours. 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 by 30 hours 
C)  increase available hours for assembly time by 40 hours 
D)  decrease available hours for assembly time by 5 hours 
E)  increase available hours for assembly time by 5 hours 
A)  do not change available hours for assembly time 
B)  decrease available hours for assembly time by 30 hours 
C)  increase available hours for assembly time by 40 hours 
D)  decrease available hours for assembly time by 5 hours 
E)  increase available hours for assembly time by 5 hours

Question 20

Consider the following constraints from a two-variable linear program: X ≥ 1; Y ≥ 1; X + Y ≤ 9. If these are the only constraints, which of the following points (X, Y) CANNOT be the optimal solution?

Accepted Answer

A)  (1, 1) 
B)  (1, 8) 
C)  (8, 1) 
D)  (4, 4) 
E)  The question cannot be answered without knowing the objective function. 
A)  (1, 1) 
B)  (1, 8) 
C)  (8, 1) 
D)  (4, 4) 
E)  The question cannot be answered without knowing the objective function.

Which of the following sets of constraints results in an unbounded maximization problem?

The feasible region in the diagram below is consistent with which one of the following constraints?

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

The corner-point solution method requires:

________ variables allow us to introduce "yes-or-no" decisions into our linear programs and to introduce special logical conditions.

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

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

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 correctly describes all iso-profit lines for an LP maximization problem?

If we wish to ensure that decision variable values in a linear program are integers rather than fractions, the generally accepted practice is to round the solutions to the nearest integer values.

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

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 diet problem is known in agricultural applications as the:

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

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

Identify three examples of resources that are typically constrained in a linear programming problem.

Consider the following constraints from a two-variable linear program: X ≥ 1; Y ≥ 1; X + Y ≤ 9. If these are the only constraints, which of the following points (X, Y) CANNOT be the optimal solution?

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Exam 18: Linear Programming

Which of the following sets of constraints results in an unbounded maximization problem?

The feasible region in the diagram below is consistent with which one of the following constraints?

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

The corner-point solution method requires:

________ variables allow us to introduce "yes-or-no" decisions into our linear programs and to introduce special logical conditions.

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

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

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 correctly describes all iso-profit lines for an LP maximization problem?

If we wish to ensure that decision variable values in a linear program are integers rather than fractions, the generally accepted practice is to round the solutions to the nearest integer values.

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

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 diet problem is known in agricultural applications as the:

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

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

Identify three examples of resources that are typically constrained in a linear programming problem.

Consider the following constraints from a two-variable linear program: X ≥ 1; Y ≥ 1; X + Y ≤ 9. If these are the only constraints, which of the following points (X, Y) CANNOT be the optimal solution?

Operations and Productivity

Operations Strategy in a Global Environment

Project Management

Forecasting

Design of Goods and Services

Managing Quality

Process Strategies

Location Strategies

Human Resources, Job Design, and Work Measurement

Supply Chain Management

Inventory Management

Aggregate Planning and Sop

Material Requirements Planning Mrp and Erp

Short-Term Scheduling

Lean Operations

Maintenance and Reliability

Decision-Making Tools

Transportation Models

Waiting-Line Models

Learning Curves

Simulation

Applying Analytics to Big Data in Operations Management

Filters