Step 1: Identify the Objective Function

The objective function is given by Z = 4x + 3y. We need to evaluate this function at each of the provided corner points of the feasible region.

Step 2: Evaluate Z at each corner point

We substitute the coordinates (x, y) into the objective function:

• At (0, 0): Z = 4(0) + 3(0) = 0
• At (0, 40): Z = 4(0) + 3(40) = 120
• At (20, 40): Z = 4(20) + 3(40) = 80 + 120 = 200
• At (60, 20): Z = 4(60) + 3(20) = 240 + 60 = 300
• At (60, 0): Z = 4(60) + 3(0) = 240

Step 3: Determine the Maximum Value

Comparing the calculated values {0, 120, 200, 300, 240}, the maximum value is 300, which occurs at the point (60, 20).