If $(0, 0), (30, 0), (20, 30)$ and $(0, 50)$ are the vertices of the feasible region of the LPP
Maximize $Z = 60 x + 50 y$
Subject to $x + y \geq 50, 3 x + y \leq 90$ and $x, y \geq 0$ , then $Z_{m a x} =$

2500

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3000

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2700

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1800

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Solution

The correct option is B $2700$
$Z = 60 x + 50 y$
at $(0, 0)$ $Z = 0$
at $(30, 0)$ $Z = 60 \times 30 + 0 = 1800$
at $(20, 30)$ $Z = 60 \times 20 + 50 \times 30 = 2700$
at $(0, 50)$ $Z = 0 + 50 \times 50 = 2500$
$∴$ $Z_{m a x} = 2700$
$∴$ (3) is correct

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