By graphical method solve the following linear programming problem for minimization:
Objective function constraints $Z = 5 x + y$
$3 x + 5 y \geq 5$
$5 x + 2 y \leq 10$
$x \geq 0, y \geq 0$

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Solution

Function to minimize: $Z = 5 x + y$
Constraints: $3 x + 5 y \geq 5$
$5 x + 2 y \leq 10$
$x \geq 0, y \geq 0$

Cornor Points Values of $Z = 5 x + y$ at cornor points
$(0, 1)$ $1 \leftarrow$ Minimum
$(0, 5)$ $5$
$(2, 0)$ $10$
$(\frac{5}{2}, 0)$ $\frac{25}{3}$
Hence, the minimum value of $Z = 5 x + y$ is $1$ .

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Similar questions

3 x + 5 y \leq 5; 5 x + 2 y \leq 10; x \geq 0, y \geq 0

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Cornor Points	Values of $Z = 5 x + y$ at cornor points
$(0, 1)$	$1 \leftarrow$ Minimum
$(0, 5)$	$5$
$(2, 0)$	$10$
$(\frac{5}{2}, 0)$	$\frac{25}{3}$