Question

The maximum value of \( z = 3x + 5y \), subject to \( 3x + 2y \leq 18 \), \( x \leq 4 \), \( y \leq 6 \), \( x, y \geq 0 \) is

• A. 30
• B. 27
• C. 36
• D. 32

Hint:

In linear programming, the maximum or minimum value of the objective function occurs at one of the corner points of the feasible region.

Answer 1

The Correct Option is C

Step 1: Set up the constraints.
We are given a set of linear constraints and we need to maximize the objective function \( z = 3x + 5y \). We first graph the constraints and identify the feasible region.

Step 2: Check the corner points.
The maximum value of \( z \) occurs at one of the corner points of the feasible region. After evaluating the objective function at each corner point, we find that the maximum value of \( z \) is 36.

Step 3: Conclusion.
Thus, the maximum value of \( z \) is 36, corresponding to option (C).