Linear Programming and Objective Function

Topics: Linear programming, Optimization, Operations research Pages: 37 (3484 words) Published: November 13, 2013
 Q.No.
 Question
 Options
 Answer
 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.
 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 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...
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