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Absolute Value Function

Solve the fol...

Question

Solve the following Linear Programming Problem graphically:
Maximize $Z = 5 x + 3 y$
Subject to:
$3 x + 5 y \leq 15, 5 x + 2 y \leq 10,$
$x \geq 0, y \geq 0$

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Solution

Maximize $Z = 5 x + 3 y$
Subject to
$3 x + 5 y \leq 15, 5 x + 2 y \leq 10,$ $x \geq 0, y \geq 0$

$3 x + 5 y = 15$
$\begin{matrix} x & 0 & 5 y & 3 & 0 \end{matrix}$

$5 x + 2 y = 10$
$\begin{matrix} x & 0 & 2 y & 5 & 0 \end{matrix}$
$\begin{matrix} Corner points & Value of Z = 5 x + 3 y (0, 3) & 9 (\frac{20}{19}, \frac{45}{19}) & \frac{235}{19} (2, 0) & 10 \end{matrix}$

Hence, $Z = \frac{235}{19}$ is maximum at $(\frac{20}{19}, \frac{45}{19})$ .

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Absolute Value Function

Standard XII Mathematics

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