The feasible region of an LPP is shown in the figure.
If $Z = 5 x + 2 y,$ then the maximum value of $Z$ occurs at

$(a) (0, 0) (b) (5, 0)$
$(c) (2, 4) (d) (0, 4)$

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Solution

$\begin{matrix} Corner Point & Z = 5 x + 2 y (0, 0) & 5 \times 0 + 2 \times 0 = 0 (5, 0) & 5 \times 5 + 2 \times 0 = 25 (2, 4) & 5 \times 2 + 2 \times 4 = 18 (0, 4) & 5 \times 0 + 2 \times 4 = 8 \end{matrix}$
Maximum value of $Z = 25$ which occurs at $(5, 0) .$

$∴$ Option $(b)$ is correct.

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