Question

Solve the following linear programming problem graphically:
Minimize $Z=200x+500y$
Subject to the constraints:
$x+2y\ge 10$
$3x+4y\le 24$
$x\ge 0,y\ge 0$

Answer 1

Minimise $Z=200x+500y$
Subject to
$x+2y\ge 10$, $3x+4y\le 24$, $x\ge 0,y\ge 0$

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

$3x+4y=24$
$\begin{array}{ccc}x& 0& 8\\ y& 6& 0\end{array}$
$\begin{array}{cc}\text{Corner points}& \text{Value of}Z=200x+500y\\ (0,6)& 3000\\ (0,5)& 2500\\ (4,3)& 2300\end{array}$

$\therefore$ Minimum value of $z$ is $2300$ at $(4,3)$.