Question

Maximize:Z=x+2y
Subject to the constraints:$x+2y\ge 100,2x-y\le 0,2x+y\le 200,x\ge 0,y\ge 0$
Solve the L.P.P. graphically.

Answer 1

To Maximize:Z=x+2y

Subject to : $x+2y\ge 100,2x-y\le 0,2x+y\le 200,x\ge 0,y\ge 0$

$\begin{array}{cc}\text{Corner Points}& \text{Value of Z}\\ \text{A(0,200)}& 400\leftarrow \text{Max.value}\\ \text{B(50,100)}& 250\\ \text{C(20,40)}& 100\\ \text{D(0,50)}& 100\end{array}$
Clearly,Maximum value of Z=400 at A(0,200).