Linear Programming and Objective Function
Question
Options
Answer
1.
A negative dual price for a constraint in a minimization problem means 1.
as the righthand side increases, the objective function value will decrease. 1
2.
as the righthand side decreases, the objective function value will decrease.
3.
as the righthand side increases, the objective function value will increase.
4.
as the righthand 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 ndimensional: 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 righthand 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 righthandside values for which the objective function value will not change. 3
2.
the righthandside values for which the values of the decision variables will not change.
3.
the righthandside 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.
Shadow prices
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 righthand 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...
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