Maximise the function Z =11x +7y, subject to the constraints $x \leq 3, y \leq 2, x \leq 0$ and $y \leq 0$

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Maximise Z =11x +7y, subject to the constraints $x \leq 3, y \leq 2, x \leq 0$ and $y \leq 0$

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.

$\begin{matrix} Corner points & Corresponding value of Z (0, 0) & 0 (3, 0) & 33 (3, 2) & 4 \leftarrow Maximum (0, 2) & 47 \end{matrix}$
Hence, Z is maximum at (3,2) and its maximum value is 47.

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

Z = 3 x + 4 y

x + y \leq 4, x \geq 0, y \geq 0.

Maximise Z = 3x + 4y

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z = 5 x + 2 y

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