Consider the following linear programming problem:
MIN Z =&emsp; &emsp; 3x1 + 2x2
Subject to:&emsp; &emsp; 2x1 + 3x2 ? 12
&emsp; &emsp;&emsp;5x1 + 8x2 ? 37
&emsp; &emsp;&emsp;x1, x2 ? 0
At the optimal solution point, the objective function value is 18. If the constraints are changed from greater than to less than constraints and the objective function is changed from minimize to maximize, what happens to the optimal solution? Demonstrate whether it falls at the same optimal point.

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The Answer of Consider the following linear programming problem:
MIN Z =&emsp; &emsp; 3x1 + 2x2
Subject to:&emsp; &emsp; 2x1 + 3x2 ? 12
&emsp; &emsp;&emsp;5x1 + 8x2 ? 37
&emsp; &emsp;&emsp;x1, x2 ? 0
At the optimal solution point, the objective function value is 18. If the constraints are changed from greater than to less than constraints and the objective function is changed from minimize to maximize, what happens to the optimal solution? Demonstrate whether it falls at the same optimal point.

Consider the Following Linear Programming Problem