Maximize the function $Z = 11x + 7y$, subject to the constraints: $x ≤ 3, y ≤ 2, x ≥ 0, y≥ 0$.

47

The correct answer is Option (3) → 47

Graph the constraints

• $x = 3$ → vertical line through $x=3$
• $y = 2$ → horizontal line through $y=2$
• $x≥0,  y≥0$ → first quadrant

The shaded region as shown in the figure as OABC is bounded and the coordinates of corner points are (0 , 0), (3, 0), (3, 2) and (0, 2), respectively.

Hence, Z is maximum at (3, 2) and its maximum value is 47.