Quiz on Linear Programming Models: Graphical and Computer Methods

Pages: 17 (2781 words) Published: January 11, 2015

Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair) Chapter 2 Linear Programming Models: Graphical and Computer Methods

2.1 Chapter Questions

1) Consider the following linear programming model:
MaxX12 + X2 + 3X3
Subject to:
X1 + X2 ≤ 3
X1 + X2 ≤ 1
X1, X2 ≥ 0
This problem violates which of the following assumptions?
A) certainty
B) proportionality
C) divisibility
D) linearity
E) integrality
Answer: D
Page Ref: 22
Topic: Developing a Linear Programming Model
Difficulty: Easy

2) Consider the following linear programming model:
Min2X1 + 3X2
Subject to:
X1 + 2X2 ≤ 1
X2 ≤ 1
X1 ≥ 0, X2 ≤ 0
This problem violates which of the following assumptions?
A) additivity
B) divisibility
C) non-negativity
D) proportionality
E) linearity
Answer: C
Page Ref: 21
Topic: Developing a Linear Programming Model
Difficulty: Easy
3) A redundant constraint is eliminated from a linear programming model. What effect will this have on the optimal solution? A) feasible region will decrease in size
B) feasible region will increase in size
C) a decrease in objective function value
D) an increase in objective function value
E) no change
Answer: E
Page Ref: 36
Topic: Special Situations in Solving Linear Programming Problems Difficulty: Moderate

4) Consider the following linear programming model:
Max2X1 + 3X2
Subject to:
X1 ≤ 2
X2 ≤ 3
X1 ≤ 1
X1, X2 ≥ 0
This linear programming model has:
A) alternate optimal solutions
B) unbounded solution
C) redundant constraint
D) infeasible solution
E) non-negative solution
Answer: C
Page Ref: 36
Topic: Special Situations in Solving Linear Programming Problems Difficulty: Moderate

5) A linear programming model generates an optimal solution with fractional values. This solution satisfies which basic linear programming assumption? A) certainty
B) divisibility
C) proportionality
D) linearity
E) non-negativity
Answer: B
Page Ref: 22
Topic: Developing a Linear Programming Model
Difficulty: Moderate
6) Consider the following linear programming model:
MaxX1 + X2
Subject to:
X1 + X2 ≤ 2
X1 ≥ 1
X2 ≥ 3
X1, X2 ≥ 0
This linear programming model has:
A) alternate optimal solution
B) unbounded solution
C) redundant constraint
D) infeasible solution
E) unique solution
Answer: D
Page Ref: 37
Topic: Special Situations in Solving Linear Programming Problems Difficulty: Easy

7) Consider the following linear programming model
Max 2X1 + 3X2
Subject to:
X1 + X2
X1 ≥ 2
X1, X2 0
This linear programming model has:
A) redundant constraints
B) infeasible solution
C) alternate optimal solution
D) unique solution
E) unbounded solution
Answer: E
Page Ref: 39
Topic: Special Situations in Solving Linear Programming Problems Difficulty: Easy
8) Consider the following linear programming model
Min2X1 + 3X2
Subject to:
X1 + X2 ≥ 4
X1 ≥ 2
X1, X2 0
This linear programming model has:
A) unique optimal solution
B) unbounded solution
C) infeasible solution
D) alternate optimal solution
E) redundant constraints
Answer: A
Page Ref: 38
Topic: Special Situations in Solving Linear Programming Problems Difficulty: Easy
Figure 1:

Figure 1 demonstrates an Excel spreadsheet that is used to model the following linear programming problem:
Max:4 X1 + 3 X2
Subject to:
3 X1 +5 X2 ≤ 40
12 X1 + 10 X2 ≤ 120
X1 ≥ 15
X1, X2 ≥ 0

Note: Cells B3 and C3 are the designated cells for the optimal values of X1 and X2, respectively, while cell E4 is the designated cell for the objective function value. Cells D8:D10 designate the left-hand side of the constraints.

9) Refer to Figure 1. What formula should be entered in cell E4 to compute total profitability? A) =SUMPRODUCT(B5:C5,B2:C2)
B) =SUM(B3:C3)
C) =B2*B5 + C2*C5
D) =SUMPRODUCT(B5:C5,E8:E10)
E) =B3*B5 + C3*C5
Answer: E
Page Ref: 42
Topic: Setting Up and Solving Linear Programming Problems...
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