Maximize the function $Z = 11x + 7y$, subject to the constraints: $x ≤ 3, y ≤ 2, x ≥ 0, y≥ 0$.
Answer & explanation
Correct answer: option 3
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.
|
Corner points |
Corresponding value of $Z=11x+7y$ |
|
(0, 0) |
0 |
|
(3, 0) |
33 |
|
(3, 2) |
47 → Maximum |
|
(0, 2) |
14 |
Hence, Z is maximum at (3, 2) and its maximum value is 47.