1 answer

Consider the following linear programming problem. Maximize 5X1 + 3X2 Subject to: X1 + X2 ≤...

Question:

Consider the following linear programming problem.

Maximize 5X1 + 3X2 Subject to: X1 + X2 ≤ 20 X1 ≥ 5 X2 ≤ 10 X1, X2 ≥ 0

What are the optimal values of X1 and X2 respectively?


Answers

Solution: Problem is Max Z = 5x1 + 3X2 subject to X1 + X2 s 20 Xi 25 X2<10 and x1, x2 = 0; The problem is converted to canoniIteration-1 MinRatio 1 = 20 Z= -5M Z;- ; - M-51 Negative minimum z- CIS - M - 5 and its column index is 1. So, the entering v+ Rz(new) = Rz(old) + R(new) = R. (old) - Rz (new) + R3(new) = R3(old) Iteration 2 530 MinRatio B CB = 15 X Sz Z = 25 5 5 100Negative minimum 2; -; is - 5 and its column index is 4. So, the entering variable is S2 Minimum ratio is 15 and its row indeSince all Z:-C;20 Hence, optimal solution is arrived with value of variables as: X 1 = 20,X2 = 0 Max Z = 100

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