# Linear Programming and Objective Function

Pages: 37 (3484 words) Published: November 13, 2013
﻿ Q.No.
Question
Options
1.
A negative dual price for a constraint in a minimization problem means  1.
as the right-hand side increases, the objective function value will decrease.  1

2.
as the right-hand side decreases, the objective function value will decrease.

3.
as the right-hand side increases, the objective function value will increase.

4.
as the right-hand side decreases, the objective function value will increase.

5.
-

1.
Which of the following is not true about slack variables in a simplex tableau?  1.
They are used to convert ≤ constraint inequalities to equations.  3

2.
They represent unused resources.

3.
They require the addition of an artificial variable.

4.
They yield no profit.

5.
-

2.
In Linear Programming Problems (LPP) with three or more variables, the area of feasible solutions is known as an n-dimensional:  1.
Pentagon
4

2.
Octagon

3.
Polyhydra

4.
Polyhedron

5.
-

2.
A constraint with a negative slack value
1.
will have a positive dual price.
3

2.
will have a negative dual price.

3.
will have a dual price of zero.

4.
has no restrictions for its dual price.

5.
-

3.
The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the  1.
optimal solution.
3

2.
dual solution.

3.
range of optimality.

4.
range of feasibility.

5.
-

3.
In Linear Programming Problems, if a constraint is presented by the inequality, 5X - 2Y ≥ 8, how this can be converted into simplex tableau form? (Symbols have usual meaning)  1.
5X - 2Y + S + A = 8
2

2.
5X - 2Y - S + A = 8

3.
5X - 2Y - S = 8

4.
5X - 2Y + A = 8

5.
-

4.
Let us consider the general form of a linear programming problem as given below:

Maximize Profit
Subject to: Amount of Resource 1 used ≤ 100 units
Amount of Resource 2 used ≤ 240 units
Amount of Resource 3 used ≤ 150 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? (Symbols have usual meaning)  1.

It would not change.
3

2.
It would decrease by 140.

3.
It would increase by 40.

4.
It would decrease by 40.

5.
-

4.
The range of feasibility measures
1.
the right-hand-side values for which the objective function value will not change.  3

2.
the right-hand-side values for which the values of the decision variables will not change.

3.
the right-hand-side values for which the dual prices will not change.

4.
each of the above is true.

5.
-

5.
Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then  1.
B ≤ 5
3

2.
A - .5B + C ≤ 0

3.
-.5A + .5B - .5C ≤ 0

4.
.5A - B - .5C ≤ 0

5.
-

5.
1.
Can be derived from the coefficients of the slack variables in the Zj - Cj row of an optimal simplex tableau.  4

2.
Represent the value of one additional unit of a resource.

3.
Are found in the solution to the dual LP.

4.
All of the above

5.
-

6.
The 100% Rule compares
1.
proposed changes to allowed changes.
1

2.
new values to original values.

3.
objective function changes to right-hand side changes.

4.
dual prices to reduced costs.

5.
-

6.
A slack variable
1.
Is added to each ≤ constraint to facilitate the simplex process.  1

2.
Is added to each ≥ constraint to facilitate the simplex process.

3.
Is added to each ≤ or = constraint to facilitate the simplex process.

4.
Is...