Solutions Operations management

You are using the simplex method to solve the following linear programming problem. Maximize Z = 6

Question: You are using the simplex method to solve the following linear programming problem.

Maximize Z = 6x1 + 5x2 - x3 + 4x4,

subject to

3x1 + 2x2 - 3x3 + x4 ≤ 120

3x1 + 3x2 + x3 + 3x4 ≤ 180

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0.

You have obtained the following final simplex tableau where x5 and x6 are the slack variables for the respective constraints.

Coefficient of:
Basic Variable Eq. Z x1 x2 x3 x4 x5 x6 Right Side
Z (0) 1 0 \[\frac{1}{4}\] 0 \[\frac{1}{2}\] \[\frac{3}{4}\] \[\frac{5}{4}\] Z*
x1 (1) 0 1 \[\frac{11}{12}\] 0 \[\frac{5}{6}\] \[\frac{1}{12}\] \[\frac{1}{4}\] \[b_{1}^{*}\]
x3 (2) 0 0 \[\frac{1}{4}\] 1 \[\frac{1}{2}\] -\[\frac{1}{4}\] \[\frac{1}{4}\] \[b_{2}^{*}\]

Use the fundamental insight presented in Sec. 5.3 of the textbook to identify Z*, \[b_{1}^{*}\], and \[b_{2}^{*}\].

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Answer: The answer consists of 1 page
Solution Format: Word Document


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