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Solution of Inequations

Solve the fol...

Question

Solve the following Linear Programming Problem graphically:
Maximize $Z = 3 x + 2 y$
Subject to $x + 2 y \leq 10, 3 x + y \leq 15, x, y \geq 0$

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Solution

Maximise $Z = 3 x + 2 y$
Subject to
$x + 2 y \leq 10, 3 x + y \leq 15, x, y \geq 0$

$x + 2 y = 10$
$\begin{matrix} x & 0 & 10 y & 5 & 0 \end{matrix}$

$3 x + y = 15$
$\begin{matrix} x & 0 & 5 y & 15 & 0 \end{matrix}$
$\begin{matrix} Corner points & Value of Z = 3 x + 2 y (5, 0) & 15 (4, 3) & 18 (0, 5) & 10 (0, 0) & 0 \end{matrix}$

Hence, $Z = 18$ is maximum at $(4, 3)$ .

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Solution of Inequations

Standard VII Mathematics

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