Solve the following linear programming problem by graphical method:
Maximize $Z = 3 x + 2 y$
subject to the in constraints
$x + 2 y \leq 10, 3 x + y \leq 15, x, y \geq 0$

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Solution

Function to Maximize: $Z = 3 x + 2 y$
Constraints: $x + 2 y \geq 10$
$3 x + y \leq 15$
$x \geq 0, y \geq 0$

Cornor Points Values of $Z = 3 x + 2 y$ at cornor points
$(0, 0)$ $0$
$(0, 5)$ $10$
$(4, 3)$ $18 \leftarrow$ Maximum
$(5, 0)$ $15$
Hence, the Maximum value of $Z = 3 x + 2 y$ is $18$ .

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Cornor Points	Values of $Z = 3 x + 2 y$ at cornor points
$(0, 0)$	$0$
$(0, 5)$	$10$
$(4, 3)$	$18 \leftarrow$ Maximum
$(5, 0)$	$15$