Chapter 6 Integer, Goal, and Nonlinear Programming Models

6.1 Chapter Questions

1) These are problems in which some, but not all, the decision variables must have integer solutions:

A) mixed IP problems

B) pure IP problems

C) pure binary problems

D) mixed binary IP problems

E) goal programming problems

Answer: A

Page Ref: 212

Topic: Introduction

Difficulty: Easy

2) These are problems in which all decision variables must have integer solutions:

A) mixed binary IP problems

B) pure binary IP problems

C) mixed IP problems

D) pure IP problems

E) goal programming problems

Answer: D

Page Ref: 212

Topic: Introduction

Difficulty: Easy

3) Rounding off the solution to an LP relaxed problem may yield:

A) an infeasible solution

B) a non-optimal solution

C) a higher objective function value

D) an unbounded solution

E) A or B

Answer: E

Page Ref: 212

Topic: Models with General Integer Variables

Difficulty: Moderate

4) A company wants to select 2 products from a set of four possible products. Which of the following constraints ensures that no more than 3 will be selected?

A) XA + XB + XC + XD = 3

B) XA + XB + XC + XD ≥ 0

C) XA + XB + XC + XD ≤ 3

D) XA + XB + XC + XD ≥ 3

E) XA + XB + XC + XD ≠ 3

Answer: C

Page Ref: 222

Topic: Models with Binary Variables

Difficulty: Moderate

5) A company wants to select one product from a set of 3 possible products. Which of the following ensures that only one product will be selected?

A) XA + XB + XC = 1

B) XA + XB + XC ≤ 1

C) XA + XB + XC ≥ 1

D) XA + XB + XC ≥ 0

E) XA - XB - XC = 1

Answer: A

Page Ref: 222

Topic: Models with Binary Variables

Difficulty: Moderate

6) If a company produces product A then it must also produce either product B or product C. Which of the following constraints enforces this condition?

A) XA - XB - XC ≥ 0

B) XA + XB + XC ≤ 2

C) XA + (XB - XC) ≤ 0

D) XA + XB + XC ≥ 2

E) XA - XB - XC ≤ 0

Answer: E

Page Ref: 222

Topic: Models with Binary Variables

Difficulty: Moderate

7) Which type of cost is independent of the volume of production?

A) inventory cost

B) marginal cost

C) sunk cost

D) variable cost

E) fixed charge

Answer: E

Page Ref: 226

Topic: Mixed Integer Models: Fixed-Charge Problems

Difficulty: Easy

8) A company incurs a cost that is directly proportional to the magnitude of the decision variable. This is an example of a:

A) fixed charge

B) sunk cost

C) variable cost

D) marginal cost

E) inventory cost

Answer: C

Page Ref: 226

Topic: Mixed Integer Models: Fixed-Charge Problems

Difficulty: Easy

9) Consider a model with 3 ranked goals. Solving this model requires us to solve:

A) a single LP problem

B) 3 separate LP problems

C) 2 separate LP problems

D) a single quadratic programming problem

E) 3 quadratic programming problems

Answer: B

Page Ref: 238

Topic: Goal Programming Models

Difficulty: Moderate

10) If a company produces Product A, then it must produce at least 200 units of Product A. Which of the following constraints model this condition?

A) X1Y1 ≤ 200

B) X1 ≥ 200 + Y1

C) X1 ≤ 200Y1

D) X1 - 200Y1 ≥ 0

E) X1 > 200

Answer: D

Page Ref: 244

Topic: Nonlinear Programming Models

Difficulty: Moderate

11) An investment strategy restricts the portfolio to a mix of two stocks A and B with the following price/share and annual returns:

Stock Price/Share Annual Return A $35 5% B $45 7%

Assume that the maximum amount available for investment is $100,000 with the following 2 prioritized investment goals:

Rank R1: Obtain an annual return of at least 6%.

Rank R2: Limit the investment in stock B to no more than 55% of the total investment.

Assume X1 = dollar amount allocated to stock A, and X2 = dollar amount allocated to stock B.

What is the objective function?

A) Min d1+ + d2-

B) Min R2(d1+) + R1(d2-)

C) Min R1(d1-) - R2(d2+)

D) Min R1(d1+) + R2(d2-)

E) Min R1(d1-) + R2(d2+)

Answer: E

Page Ref: 237

Topic: Goal Programming Models

Difficulty: Moderate

12)