Module 7 Linear Programming: The Simplex Method

33) The dual problem formulation can be
solved using the same simplex process used for the primal formulation.
Diff: 2
Topic: THE DUAL

34) The substitution rates give
A) the number of units of each basic
variable that must be removed from the solution if a new variable is entered.
B) the gross profit or loss given up by
adding one unit of a variable into the solution.
C) the net profit or loss that will result
from introducing one unit of the variable indicated in that column into the
solution.
D) the maximal value a variable can take
on and still have all the constraints satisfied.
E) None of the above
Diff: 2
Topic: HOW TO SET UP THE INITIAL SIMPLEX SOLUTION

35) In 1984, who developed an alternative
to the simplex algorithm, which often takes significantly less computer time to
solve very large-scale LP problems?
A) Carmichael
B) Kruskev
C) Karmarkar
D) Krakov
E) Carpenter
Diff: 2
Topic: KARMARKAR’S ALGORITHM

36) Which of the following is not
true about slack variables in a simplex tableau?
A) They are used to convert ? constraint
inequalities to equations.
B) They represent unused resources.
C) They require the addition of an
artificial variable.
D) They may represent machine time, labor
hours, or warehouse space.
E) They yield no profit.
Diff: 2
Topic: HOW TO SET UP THE INITIAL SIMPLEX SOLUTION

37) How does Karmarkar’s Algorithm differ
from the simplex method?
A) It follows a path of integer solutions.
B) It follows a path inside the feasible
region.
C) It follows a counterclockwise path
around the outside edges of the feasible region.
D) It follows a clockwise path around the
outside edges of the feasible region.
E) It incorporates a second set of
artificial variables.
Diff: 2
Topic:
KARMARKAR’S ALGORITHM

38) In LP problems with more than two variables,
the area of feasible solutions is known as an
n-dimensional
A) pentagon.
B) cube.
C) octagon.
D) hydra.
E) polyhedron.
Diff: 2
Topic: INTRODUCTION

39) How should the constraint, 5X – 2Y ?
6, be converted into simplex tableau form?
A) 5X – 2Y + S + A = 6
B) 5X – 2Y – S + A = 6
C) 5X – 2Y – S = 6
D) 5X – 2Y + A = 6
E) 5X – 2Y + S ? A = 6
Topic: SURPLUS AND ARTIFICIAL VARIABLES
AACSB: Analytic Skills

40) Consider the following general form of
a linear programming problem:

Maximize Profit
Subject to: Amount of resource A used ? 100 units
Amount of resource B
used ? 240 units
Amount of resource C
used ? 50 units

The shadow price for S1 is 25, for S2 is 0, and for S3 is 40. If the right-hand side of constraint 3
were changed from 150 to 151, what would happen to maximum possible profit?

A) It would not change.
B) It would increase by 25.
C) It would decrease by 25.
D) It would increase by 40.
E) It would decrease by 40.
Diff: 2
Topic:
SENSITIVITY ANALYSIS WITH THE SIMPLEX TABLEAU

Table M7-1

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41) According to Table M7-1, all of the
resources are being used. If the amount of resource A were changed from 64 to
65, then the maximum possible total profit would be
A) 416.
B) 417.
C) 416.5.
D) 415.5.
E) None of the above
Diff: 2
Topic: SENSITIVITY ANALYSIS WITH THE SIMPLEX TABLEAU
AACSB: Analytic Skills

42) According to Table M7-1, all of the
resources are being used. If the amount of resource B were changed from 96 to
97, then the maximum possible total profit would be
A) 416.
B) 417.
C) 419.
D) 420.
E) None of the above
Diff: 2
Topic: SENSITIVITY ANALYSIS WITH THE SIMPLEX TABLEAU
AACSB: Analytic Skills