Determine the maximum value of $Z=11x+7y$ subject to the constraints: $2x + y ≤6,x≤2,x≥0,y≥0$.

42

The correct answer is Option (2) → 42

Given that: $Z=11x+7y$ and the constraints $2x+y≤6,x≤2, x≥0,y≥0$.

Let $2x+y=6$

The shaded area OABC is the feasible region determined by the constraints $2x+y≤6,x≤2,x≥0, y≥0$.

The feasible region is bounded.

So, maximum value will occur at a corner point of the feasible region.

Corner points are (0, 0), (2, 0), (2, 2) and (0,6).

Now, evaluating the value of Z, we get

Hence, the maximum value of Z is 42 at (0, 6).