By graphical method solve the following linear programming problem for maximization.
Objective function Z = 1000 x + 600 y
Constraints $x + y \leq 200$
$4 x - y \leq 0$
$x \geq 20, x \geq 0, y \geq 0$ .

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Solution

Function to maximize: $Z = 1000 x + 600 y$
Constraints: $x + y \leq 200$
$4 x - y \leq 0$
$x \geq 20$
$x \geq 0, y \geq 0$

Corner Points Values of $Z = 1000 x + 600 y$ at corner points
$(20, 80)$ $68000$
$(20, 180)$ $110000$
$(40, 160)$ $136000 \leftarrow$ Maximum
Hence, the maximum value of $Z = 1000 x + 600 y$ is $136000$ .

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Similar questions

Z = 5 x + y

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5 x + 2 y \leq 10

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z = 3 x + 4 y

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Z = 3 x + 2 y

x + 2 y \leq 10, 3 x + y \leq 15, x, y \geq 0

Z = 3 x + 5 y

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Corner Points	Values of $Z = 1000 x + 600 y$ at corner points
$(20, 80)$	$68000$
$(20, 180)$	$110000$
$(40, 160)$	$136000 \leftarrow$ Maximum