Sensitivity analysis, Which constraints are binding and

Sensitivity analysis

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Reference no: EM132216885

Assessment – Sensitivity Analysis

In a product-mix-problem, X1, X2, X3, and X4 indicate the units of products 1, 2, 3, and 4, respectively, and the linear programming model is

MAX Z = $15X1+$17X2+$18X3+$16X4

S.T.

1) 5X1+3X2+8X3+4X4 £ 1600 Machine A hours

2) 7X1+8X2+7X3+6X4 £ 1700 Machine B hours

3) 2X1+9X2+1X3+2X4 £ 1800 Machine C hours

4) 6X1+2X2+6X3+5x4 £ 1900 Machine D hours

Input the data in an Excel file and save the file. Using Solver, solve the problem and obtain sensitivity results.

Questions:

What is the value of maximum profit?

Which constraints are binding and what does it mean?

Which machines have excess capacity available? How much?

If the objective function coefficient of X1 is increased by $0.50, will the optimal solution change? What would be the new value of the objective function?

Suppose the objective function coefficient of X1 is increased by 0.80, the objective function coefficient of X2 is decreased by 1.1, and the objective function coefficient of X4 is increased by 0.4, what will be the new optimal solution and the value of the objective function? Explain and show your computations to support your answer.

What should be the contribution of product 4, so it will be profitable to produce? Explain.

Seven hundred additional hours for Machine B can be obtained at 1.10 above the current cost. Should the additional hours be obtained at the quoted cost? Why or why not? Fully explain. If the 500 additional Machine A hours are obtained, what will be the net increase in profits?

One hundred additional hours for Machine A can be obtained free of charge. Should the additional hours be obtained? Why or why not? Fully explain.

Reference no: EM132216885

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