Exam 3 Studyguide

What is the unit profit for the Luxury item?

$3

What is the optimal solution for the following problem?

(x, y) = (0, 2.4).

Given the following 2 constraints, which solution is a feasible solution for a minimization problem? (1) 10x1 + 5x2 ≥ 50(2) x1 + 2x2 ≥ 12

(x1, x2) = (3, 5)

What is the allowable range of the right-hand-side for Resource A?

-∞ ≤ RHSA ≤ 110

For a problem with two decision variables, which of the following statements about what-if analysis is TRUE? 1. What-if analysis can be done graphically. 2. Solver will generate reports to assist with what-if analysis. 3. Shadow prices will not be valid with only two decision variables.

1 & 2

If the objective function coefficient for Product_1 were increased to a value of 8, which of the following would be TRUE? 1. The optimal solution would change. 2. The optimal objective function value would stay the same. 3. Product_1 would enter the solution (the final value of the variable Product_1 would be greater than zero).

1 & 3

In a transportation problem with 4 sources and 6 destinations, how many fixed requirement constraints will be needed?

10 (4 + 6)

In a transportation problem with 8 sources and 2 destinations, how many fixed requirement constraints will be needed?

10 (8+2)

What is the allowable range for the objective function coefficient for Activity 3?

150 ≤ A3 ≤ ∞

To determine if an increase in an objective function coefficient will lead to a change in final values for decision variables, an analyst can do which of the following? 1. Compare the increase in the objective function coefficient to the allowable decrease. 2. Compare the increase in the objective function coefficient to the allowable increase. 3. Rerun the optimization to see if the final values change.

2 & 3 only

If the objective function coefficient for Product_1 were decreased to a value of 3, which of the following would be TRUE? 1. The optimal solution would change. 2. The optimal objective function value would stay the same. 3. Product_1 would enter the solution (the final value of the variable Product_1 would be greater than zero).

2 only

The key identifying feature of a resource-allocation problem is which of the following? 1. Constraints with the form "Amount of resource used ≥ Amount of resource available". 2. Constraints with the form "Amount of resource used ≤ Amount of resource available". 3. Constraints with the form "Level achieved ≥ Minimum acceptable level". 4. All constraints have the form "Amount provided = Required amount".

2 only

In a transportation problem with 4 sources and 5 destinations, how many shipping lanes will exist?

20 (4 × 5) shipping lanes.

In a transportation problem with 4 sources and 6 destinations, how many shipping lanes will exist?

24 (4 × 6)

Assignment problems can be classified as which type of linear programming problem? 1. Resource-allocation problems. 2. Cost-benefit-tradeoff problems. 3. Fixed-requirement problems.

3 only

The key identifying feature of a cost-benefit trade-off problem is which of the following? 1. Constraints with the form "Amount of resource used ≥ Amount of resource available". 2. Constraints with the form "Amount of resource used ≤ Amount of resource available". 3. Constraints with the form "Level achieved ≥ Minimum acceptable level". 4. All constraints have the form "Amount provided = Required amount".

3 only

Transportation problems can be classified as which type of linear programming problem? 1. Resource-allocation problems. 2. Cost-benefit-tradeoff problems. 3. Fixed-requirement problems.

3 only

The key identifying feature of a fixed-requirements problem is which of the following? Constraints with the form "Amount of resource used ≥ Amount of resource available". Constraints with the form "Amount of resource used ≤ Amount of resource available". Constraints with the form "Level achieved ≥ Minimum acceptable level". All constraints have the form "Amount provided = Required amount".

4 Only

The key identifying feature of a mixed problem is which of the following? 1. Constraints with the form "Amount of resource used ≥ Amount of resource available". 2. Constraints with the form "Amount of resource used ≤ Amount of resource available". 3. Constraints with the form "Level achieved ≥ Minimum acceptable level". 4. All constraints have the form "Amount provided = Required amount".

At least two of II, III, and IV.

Where are the decision variables located?

B2:C2 (Units Produced)

Which of the following components of a linear programming model sets limits on the set of potential solutions?

Constraints

In a linear programming problem, the changing cells do which of the following?

Contains the decisions made about levels of activity.

Where is the objective function located?

D4 (Total Profit)

Which of the following components of a linear programming model represents the level of each activity?

Decision variables

In a linear programming problem, the output cells do which of the following?

Ensures that usage of resources does not exceed available supply.

In a linear programming problem, the objective cell does which of the following?

Measures the performance of candidate solution.

Which of the following statements about what-if analysis is TRUE?

None of the answer choices is correct.

Which of the following components of a linear programming model is the overall performance measure?

Objective

In a linear programming problem, the data cells do which of the following?

Provides important information about the availability of resource.

Which of the following represents the marginal gain in the objective value that would occur if one more unit of a resource were added?

Shadow price

If the right-hand side of Resource_C increases to 750, which of the following would be true?

The objective function value will increase by $87.50

If the objective function coefficient for Product_1 were changed to 6 and the objective function coefficient for Product_3 were changed to 10, what would be the effect on the optimal solution?

The optimal solution may or may not remain the same.

Which of the following statements about feasible solutions to a linear programming problem is TRUE?

The optimal solution will also be a feasible solution.

Which of the following statements about feasible solutions to a linear programming problem is FALSE?

There will always be at least one feasible solution to any linear programming problem.

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.

True

In robust optimization, a constraint that cannot be violated is known as a

hard constraint.

A parameter in a linear programming problem is said to be "sensitive" when

small changes in the parameter lead to changes in the optimal solution.

If the right-hand side of Resource B is increased by 30, and the right-hand side of Resource C is decreased by 10, then:

the shadow prices may or may not be valid.

The process of determining the effect of changing objective function coefficients, right-hand side values of constraints, and decision variable values on a linear program is known as

what-if analysis.

Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.) (1) 10x1 + 5x2 ≥ 50 (2) 1x1 + 2x2 ≥ 12

x1 = 2.667 x2= 4.667