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# LPP:Sensitivity analysis

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The following linear programming model formulation is used for the production of four different products, with two different manufacturing processes and two different material requirements.

maximize Z = \$50 X1 + 58 X2 + 46 X3 + 62 X4
subject to

***NOTICE- The x's have no. behind them that are lowered right cased numbers. FYo for al of them seen.

4X1 + 3.5X2 + 4.6X3 + 3.9X4 less than or equal to 600 hr ( process 1)

2.1X1 + 2.6X2 + 3.5 X3 + 1.9 X4 less than or greater than 500 hr ( process 2)

15X1 + 23 X2 + 18 X3 + 25X4 less than or equal to 3,600 lb ( material A )

8X1 + 12.6 X2 + 9.7X3 + 10.5 X4 less than or equal to 1,700 lb ( material B)

X1 + X2 / X1 + X2 + X3 + X4 greater than or equal to .60
X1, X2, X3, X4 greater than or equal to 0
A. Solve this problem using the computer
B. Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values.
C. Which is the most valuable resource to the firm?
D. One of the four products is not produced in the optimal solution. How much would the profit for this product have to be for it to be produced?