Sensitivity analysis

Let x = number of units of product 1 to produce and let y = number of units of product 2 to produce. Consider the following objective function: Maximize z = x + 2y. Subject to the following constraints: x + y ≤ 12 (resource A), x ≤ 8 (resource B), y ≤ 6 (resource C), x and y ≥ 0. What will the optimal objective function value be?

• 12

• 18

• 16

• 10

Refer to Question #1. Suppose the amount resource A available is increased from 12 to 14. Now what will the optimal objective function value be?

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• 16

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• 24

Refer to Question #1. Suppose the amount resource B available is increased from 8 to 10. Now what will the optimal objective function value be?

• 16

• 22

• 18

• 20

Refer to Question #1. What is the shadow price for the resource C constraint?

• 2

• 3

• 0

• 1

Consider a scenario with an objective function Max $14X + $17Y. Assume that the value of X in the optimal solution is zero and the reduced cost for variable X is 3. At what objective function coefficient will X first become part of the optimal solution?

• 14

• 17

• 11

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Which of the following statements is true?

• Changes to an objective function coefficient will not affect the size of the feasible region.

• An equality constraint is always nonbinding.

• If a less than or equal constraint is nonbinding then its left hand side (LHS) is greater than its right hand side (RHS). 

• Shadow prices are related with primal variables.

Suppose that a MAX problem contained the following constraint: 5x + 8y ≤ 40. Then which of the following statements is true?

• For the point (8, 5), the slack for this constraint would have a value of 40.

• For the point (4, 2.5), the slack for this constraint would be a positive value.

• For the point (4, 2), the slack for this constraint would be zero.

• For the point (1, 4), the slack for this constraint would have a value of 3.

When there is a change in one of the coefficients of the objective function and yet optimal point remains as the optimal point after the change then

• the value of the new optimal objective function changes and is generally different to the original

• the value of the new optimal objective function remains the same as original

Any change in the values for the RHS (Right Hand Side) of a binding constraint of an LP problem will:

• change the slope of the objective function

• not change the feasibility region

• change the slope of the that constraint

• not change the slope of the constraint but move it parallel to the original

The shadow price is calculated to be 3 for a less than or equal to constraint in a maximization LP problem, this means:

• if the coefficient of the objective function is increase by 3 then the RHS for that constraint must be increased by 1.

• if the coefficient of the objective function is increase by 1 then the RHS for that constraint must be increased by 3.

• if the RHS for that constraint is increased by one then the optimal objective function value is increase by 3.

• if the RHS for that constraint is increased by three then the optimal objective function value is increase by 1