Exam 4: Sensitivity Analysis and the Simplex Method

When performing sensitivity analysis, which of the following assumptions must apply?

What is the optimal objective function value if X₁ is at its lower limit in the following Analytic Solver Platform sensitivity output?

The simplex method of linear programming (LP):

The allowable decrease for a constraint is

Is the optimal solution to this problem unique, or is there an alternate optimal solution? Explain your reasoning. ​

If the shadow price for a resource is 0 and 150 units of the resource are added what happens to the optimal solution?

Use slack variables to rewrite this problem so that all its constraints are equality constraints.

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. The following table summarizes the data for the problem. Suppose the farmer can purchase more fertilizer for $2.50 per pound, should he purchase it and how much can he buy and still be sure of the value of the additional fertilizer? Base your response on the following Analytic Solver Platform sensitivity output.

How many basic variables are there in a linear programming model which has n variables and m constraints?

The allowable increase for a constraint is

Exhibit 4.2 The following questions correspond to the problem below and associated Analytic Solver Platform sensitivity report. Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Robert's grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert's task somewhat by adding the following stipulations: The following LP model allows Robert to maximize his numerical grade. -Refer to Exhibit 4.2. Based on the Analytic Solver Platform sensitivity report information, Robert has been approved by his instructor to increase the total weight allowed for the project and final exam to 0.50 plus the allowable increase. When Robert re-solves his model, what will his new final grade score be?

What is the value of the slack variable in the following constraint when X₁ and X₂ are nonbasic and only non-negativity is used as simple bounds? ​ X₁ + X₂ + S₁ = 100 ​

A change in the right hand side of a constraint changes

Consider the formulation below. How many decision variables will be there after the problem has been converted to a standard form?

The slope of the level curve for the objective function value can be changed by

The Simplex method uses which of the following values to determine if the objective function value can be improved?

A variable with a final value equal to its simple lower or upper bound and a reduced cost of zero indicates that

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water both of which are in short supply. The following table summarizes the data for the problem. Based on the following Analytic Solver Platform sensitivity output, how much can the price of Corn drop before it is no longer profitable to plant corn?

Exhibit 4.1 The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report. Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons): The following is the LP model for this logistics problem. -Refer to Exhibit 4.1. Of the three percentage of effort constraints, Shipped by Truck, Shipped by Rail, and Shipped by Air, which should be examined for potential cost reduction?

Exhibit 4.1 The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report. Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons): The following is the LP model for this logistics problem. -Refer to Exhibit 4.1. Should the company negotiate for additional air delivery capacity?