Determine the maximum value of Z =11x +7y subject to the constraints $2 x + y \geq 6, x \geq 2, x \geq 0, y \geq 0$

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Solution

We have, maximise Z=11x +7y .........(i)
Subject to the constraints
$2 x + y \leq 6 . . . . . (i i)$
$x \geq 2 . . . . . . . (i i i)$
$x \geq 0, y \geq 0 . . . . . (i v)$

We see that, the feasible region as shaded determined by the system of constraints (ii) to (iv) is OABC and is bounded. So, now we shall use corner point method to determine the maximum value of Z.

$\begin{matrix} Corner points & Corresponding value of Z (0, 0) & 0 (2, 0) & 22 (2, 2) & 36 (0, 6) & 42 \leftarrow Maximum \end{matrix}$
Hence, the maximum value of Z is 42 at (0,6)

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