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AM,GM,HM Inequality

following fig...

Question

The feasible solution for a LPP is shown in following figure. Let Z=3x-4y be the objective funciton. Minimum of Z occurs at

(a)(0,0)
(b)(0,8)
(c)(5,0)
(d)(4,10)

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Solution

$\begin{matrix} Corner points & Corresponding vlaue of Z=3x-4y (0, 0) & 0 (5, 0) & 15 \leftarrow M a x i m u m (6, 5) & - 2 (6, 8) & - 14 (4, 10) & - 28 (0, 8) & - 32 \leftarrow M i n i m u m \end{matrix}$
Hence, the minimum of Z occurs at (0,8) and its minimum value is (-32).

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