Question

Solve the following linear programming problem graphically:
Maximize: $Z=60x+40y$
subject to the constraints:

$x+2y\le 12$; $2x+y\le 12$
$x+\frac{5}{4}y\ge 5;x\ge 0,y\ge 0$.

Answer 1

Function to maximize:	$Z=60x+40y$
Constraints:	$x+2y\le 12$
	$2x+y\le 12$
	$x+\frac{5}{4}y\ge 5$
	$x\ge 0,y\ge 0$

Cornor Points	Values of $Z=60x+40y$ at cornor points
$(0,4)$	$160$
$(0,6)$	$240$
$\text{(4, 4)}$	$\text{400}\leftarrow$ Maximum
$(6,0)$	$360$
$(5,0)$	$300$

Hence, the maximum value of $Z=60x+40y$ is $400$.