Maximize Z = 15X1 + 20X2Subject to12X1 + 4X2 3612X1 - 6X2 0The above linear programming problem hasa)infeasible solutionb)unbounded solutionc)alternative optimum solutionsd)degenerate solutionCorrect answer is option 'B'. Can you explain this answer?

Question

Maximize Z = 15X1 + 20X2Subject to12X1 + 4X2 >3612X1 - 6X2 < 24X1, X2 > 0The above linear programming problem hasa)infeasible solutionb)unbounded solutionc)alternative optimum solutionsd)degenerate solutionCorrect answer is option 'B'. Can you explain this answer?

Answer

To maximize Z = 15X1 + 20X2 subject to 12X1 + 4X2 ≤ c, where c is some constant:

1. Graph the inequality 12X1 + 4X2 ≤ c on a coordinate plane.

2. The feasible region will be the area below the line formed by the inequality.

3. Identify the corner points of the feasible region. These are the points where the line intersects the x and y axes.

4. Substitute the values of the corner points into the objective function Z = 15X1 + 20X2.

5. Calculate the value of Z for each corner point.

6. The corner point that gives the highest value of Z is the optimal solution to the problem.

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