Question 1

How can the following Linear Program be characterized?
Min X + Y
Subject to
X ≥ 20
Y ≥ -5
X + Y ≤ 23

Accepted Answer

A)  bounded and feasible 
B)  unbounded and feasible 
C)  bounded and infeasible 
D)  unbounded and infeasible 
E)  this is not a Linear Program 
A)  bounded and feasible 
B)  unbounded and feasible 
C)  bounded and infeasible 
D)  unbounded and infeasible 
E)  this is not a Linear Program

Question 2

In the "Solver Options" box of Excel Solver, what should be checked to ensure that the Simplex Method is used to solve the model?

Accepted Answer

A)  Assume Non-Negative 
B)  Use Automatic Scaling 
C)  Newton 
D)  Dantzig 
E)  Assume Linear Model 
A)  Assume Non-Negative 
B)  Use Automatic Scaling 
C)  Newton 
D)  Dantzig 
E)  Assume Linear Model

Question 3

All mathematical programs should include non-negativity constraints.

Accepted Answer

A) True 
 B)False

Question 4

A specific combination of values of the decision variables such that at least one of the constraints is violated results in a(n) ______________________.

Accepted Answer

The answer of A specific combination of values of the...

Question 5

Capital Co. is considering five different projects. Define Xi as a binary (0-1) variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1,2,3,4,5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all be undertaken simultaneously?

Accepted Answer

A)  X2 + X3 + X4 ≤ 3 
B)  X1 + X2 + X3 + X4 + X5 ≤ 3 
C)  X2 + X3 + X4 ≤ 1 
D)  X2 + X3 + X4 ≤ 2 
E)  X2 + X3 ≤ 1 and X3 + X4 ≤ 1 
A)  X2 + X3 + X4 ≤ 3 
B)  X1 + X2 + X3 + X4 + X5 ≤ 3 
C)  X2 + X3 + X4 ≤ 1 
D)  X2 + X3 + X4 ≤ 2 
E)  X2 + X3 ≤ 1 and X3 + X4 ≤ 1

Question 6

Constrained optimization models can be used to either ____________ or ___________ some quantity based on a set of constraints

Accepted Answer

The answer of Constrained optimization models can be used to...

Question 7

Consider the following constraints from a two-variable Linear Program.
(1) X ≥ 0
(2) Y ≥ 0
(3) X + Y ≤ 20
(4) 2X + 5Y ≤ 70
If constraints (3) and (4) are binding, what is the optimal solution (X, Y)?

Accepted Answer

A)  (0, 20) 
B)  (20, 0) 
C)  (10, 10) 
D)  (0, 14) 
E)  (35, 0) 
A)  (0, 20) 
B)  (20, 0) 
C)  (10, 10) 
D)  (0, 14) 
E)  (35, 0)

Question 8

The Answer Report Target Cell, Adjustable Cell, and Constraint sections all include:

Accepted Answer

A)  base value, original value 
B)  original value, final value 
C)  base value, final value 
D)  original value, test value 
E)  bounded value, un-bounded value 
A)  base value, original value 
B)  original value, final value 
C)  base value, final value 
D)  original value, test value 
E)  bounded value, un-bounded value

Question 9

Formulate the following as a linear program.
Joe's Sports Shop is sponsoring a weekly boomerang-throwing contest as part of its spring promotions. Anyone may enter, but the boomerangs used must be purchased at the shop. Demand is unlimited. Two models can be made: the regular model (with a profit of $2 each) and the super model (which yields a $5 profit). However, production facilities are limited. A regular boomerang requires 1 hour of carving and 2 hours of finishing, while a super boomerang takes 3 hours to carve and 2 hours to finish. The skilled crafters employed by the shop have indicated they will spend no more than 75 hours carving and 100 hours finishing boomerangs per week. The owner wishes to allocate production in order to maximize profits.

Accepted Answer

Let R = # of regular models pr

Question 10

A diagram of the situation can help _______ the problem as well as be a(n) ______ _______ tool.

Accepted Answer

A)  structure, valuable communication 
B)  define, algebraic development 
C)  bound, formulation development 
D)  unbound, formulation development 
E)  structure, unbounded formulation 
A)  structure, valuable communication 
B)  define, algebraic development 
C)  bound, formulation development 
D)  unbound, formulation development 
E)  structure, unbounded formulation

Question 11

In Excel Solver, the Target Cell corresponds to the objective function in the algebraic model.

Accepted Answer

A) True 
 B)False

Question 12

In Linear Programming models, what do you want to do with the objective?

Accepted Answer

A)  upsize or downsize 
B)  rightsize or wrongsize 
C)  maximize or minimize 
D)  memorize 
E)  popularize 
A)  upsize or downsize 
B)  rightsize or wrongsize 
C)  maximize or minimize 
D)  memorize 
E)  popularize

Question 13

Which of the following statements is correct?

Accepted Answer

A)  Given a Linear Program with a maximization objective, the optimal objective function value may increase if a ≥ constraint is added to the program. 
B)  Given a Linear Program with a maximization objective, the optimal objective function value may increase if a ≤ constraint is added to the program. 
C)  Given a Linear Program with a minimization objective, the optimal objective function value cannot increase if a ≥ constraint is added to the program. 
D)  Given a Linear Program with a minimization objective, the optimal objective function value cannot increase if a ≤ constraint is added to the program. 
E)  Given a Linear Program with a maximization objective, the optimal objective function value may decrease if a ≥ constraint is added to the program. 
A)  Given a Linear Program with a maximization objective, the optimal objective function value may increase if a ≥ constraint is added to the program. 
B)  Given a Linear Program with a maximization objective, the optimal objective function value may increase if a ≤ constraint is added to the program. 
C)  Given a Linear Program with a minimization objective, the optimal objective function value cannot increase if a ≥ constraint is added to the program. 
D)  Given a Linear Program with a minimization objective, the optimal objective function value cannot increase if a ≤ constraint is added to the program. 
E)  Given a Linear Program with a maximization objective, the optimal objective function value may decrease if a ≥ constraint is added to the program.

Question 14

HEAVY, Inc. produces two lines of heavy equipment, earthmoving and forestry. The largest member of the earthmoving equipment line (the E-7) and the largest member of the forestry equipment line (the F-7) are produced in the same departments and with the same equipment. HEAVY's marketing manager has judged that the firm will be able to sell as many E-7s or F-7s as the firm can produce. The contribution margins are $15,000 for each E-7 and $14,000 for each F-7. There are 170 hours available in department A and 185 hours available in department B. Each E-7 produced uses 10 hours in department A and 20 hours in department B. Each F-7 uses 15 hours in department A and 10 hours in department B. Furthermore, in order to maintain the current market position, senior management has decreed that it is necessary to build at least one F-7 for every three E-7s produced. Finally, a major dealer has ordered a total of at least five E-7s and F-7s (in any combination) for next month, so at least that many must be produced. Formulate a Linear Program to determine the best production policy for next month.

Accepted Answer

Let E = # of E-7s produced
Let

Question 15

Consider the following three functions:
G(x, y) = 4x - 3y + 21
H(x, y, z) = 13x2 + y + 3z
I(z) = z
Which of the following is true regarding the linearity of the functions?

Accepted Answer

A)  none of the functions is linear 
B)  all three functions are linear 
C)  h is linear, but g and i are not linear 
D)  i is linear, but g and h are not linear 
E)  g and i are linear, but h is not linear 
A)  none of the functions is linear 
B)  all three functions are linear 
C)  h is linear, but g and i are not linear 
D)  i is linear, but g and h are not linear 
E)  g and i are linear, but h is not linear

Question 16

Consider the following two functions:
G(x, y) =4x - 3y + 21
H(x, y) = 13xy
Which of the following is true regarding the linearity of the functions?

Accepted Answer

A)  neither of the functions is linear 
B)  both functions are linear 
C)  g(x, y) is linear, but h(x, y) is not linear 
D)  h(x, y) is linear, but g(x, y) is not linear 
E)  h(x, y) is not linear, and g(x, y) is only linear when y ≥ 0 
A)  neither of the functions is linear 
B)  both functions are linear 
C)  g(x, y) is linear, but h(x, y) is not linear 
D)  h(x, y) is linear, but g(x, y) is not linear 
E)  h(x, y) is not linear, and g(x, y) is only linear when y ≥ 0

Question 17

If all constraints are not fully consumed, the final result is not an optimal solution.

Accepted Answer

A) True 
 B)False

Question 18

When is a Linear Program unbounded?

Accepted Answer

Being unbounded means that the

Question 19

Formulate the following as a linear program.
Dane's aircraft muffler manufacturers have 1000 linear feet of steel on hand to manufacture the three top selling muffler sets. Super mufflers (S) provide $35 profit and common (C) mufflers' profit margin is $31, while the deluxe (D) muffler set provides a $40 profit margin. It takes 31 hours to make the super muffler, 29 hours to manufacture the common muffler, and 40 hours to build the deluxe muffler. If Dane is limited to 200 hours a month what is the optimum combination of mufflers to manufacture to maximize his profits?

Accepted Answer

Let S -=supper muffler, C = co

Question 20

Excel Solver restricts the constraints to either >= or =.

Accepted Answer

A) True 
 B)False

How can the following Linear Program be characterized? Min X + Y Subject to X ≥ 20 Y ≥ -5 X + Y ≤ 23

In the "Solver Options" box of Excel Solver, what should be checked to ensure that the Simplex Method is used to solve the model?

All mathematical programs should include non-negativity constraints.

A specific combination of values of the decision variables such that at least one of the constraints is violated results in a(n) ______________________.

Capital Co. is considering five different projects. Define X_i as a binary (0-1) variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1,2,3,4,5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all be undertaken simultaneously?

Constrained optimization models can be used to either __ or _ some quantity based on a set of constraints

Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) X + Y ≤ 20 (4) 2X + 5Y ≤ 70 If constraints (3) and (4) are binding, what is the optimal solution (X, Y)?

The Answer Report Target Cell, Adjustable Cell, and Constraint sections all include:

A diagram of the situation can help _ the problem as well as be a(n) ___ tool.

In Excel Solver, the Target Cell corresponds to the objective function in the algebraic model.

In Linear Programming models, what do you want to do with the objective?

Which of the following statements is correct?

Consider the following three functions: G(x, y) = 4x - 3y + 21 H(x, y, z) = 13x² + y + 3z I(z) = z Which of the following is true regarding the linearity of the functions?

Consider the following two functions: G(x, y) =4x - 3y + 21 H(x, y) = 13xy Which of the following is true regarding the linearity of the functions?

If all constraints are not fully consumed, the final result is not an optimal solution.

When is a Linear Program unbounded?

Excel Solver restricts the constraints to either >= or =.

Introduction to Operations Management

Operations Strategy and Competitiveness

Product Design and Process Selection

Supply Chain Management

Total Quality Management

Statistical Quality Control

Just-In-Time and Lean Systems

Forecasting

Capacity Planning and Facility Location

Facility Layout

Work System Design

Inventory Management

Aggregate Planning

Resource Planning

Scheduling

Project Management

Spreadsheet Modeling: An Introduction

Waiting Line Models

Master Scheduling and Rough-Cut Capacity Planning

Filters

Exam 18: Introduction to Optimization

How can the following Linear Program be characterized? Min X + Y Subject to X ≥ 20 Y ≥ -5 X + Y ≤ 23

In the "Solver Options" box of Excel Solver, what should be checked to ensure that the Simplex Method is used to solve the model?

All mathematical programs should include non-negativity constraints.

A specific combination of values of the decision variables such that at least one of the constraints is violated results in a(n) ______________________.

Capital Co. is considering five different projects. Define Xi as a binary (0-1) variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1,2,3,4,5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all be undertaken simultaneously?

Constrained optimization models can be used to either ____________ or ___________ some quantity based on a set of constraints

Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) X + Y ≤ 20 (4) 2X + 5Y ≤ 70 If constraints (3) and (4) are binding, what is the optimal solution (X, Y)?

The Answer Report Target Cell, Adjustable Cell, and Constraint sections all include:

A diagram of the situation can help _______ the problem as well as be a(n) ______ _______ tool.

In Excel Solver, the Target Cell corresponds to the objective function in the algebraic model.

In Linear Programming models, what do you want to do with the objective?

Which of the following statements is correct?

Consider the following three functions: G(x, y) = 4x - 3y + 21 H(x, y, z) = 13x2 + y + 3z I(z) = z Which of the following is true regarding the linearity of the functions?

Consider the following two functions: G(x, y) =4x - 3y + 21 H(x, y) = 13xy Which of the following is true regarding the linearity of the functions?

If all constraints are not fully consumed, the final result is not an optimal solution.

When is a Linear Program unbounded?

Excel Solver restricts the constraints to either >= or =.

Introduction to Operations Management

Operations Strategy and Competitiveness

Product Design and Process Selection

Supply Chain Management

Total Quality Management

Statistical Quality Control

Just-In-Time and Lean Systems

Forecasting

Capacity Planning and Facility Location

Facility Layout

Work System Design

Inventory Management

Aggregate Planning

Resource Planning

Scheduling

Project Management

Spreadsheet Modeling: An Introduction

Waiting Line Models

Master Scheduling and Rough-Cut Capacity Planning

Filters

Capital Co. is considering five different projects. Define X_i as a binary (0-1) variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1,2,3,4,5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all be undertaken simultaneously?

Constrained optimization models can be used to either __ or _ some quantity based on a set of constraints

A diagram of the situation can help _ the problem as well as be a(n) ___ tool.

Consider the following three functions: G(x, y) = 4x - 3y + 21 H(x, y, z) = 13x² + y + 3z I(z) = z Which of the following is true regarding the linearity of the functions?