Question

Use graphical method
Maximize: $z=2x+3y$
Subject to:
$x+2y\le 40$
$6x+5y\le 150$
$x\ge 0,y\ge 0$

Answer 1

The feasible area is defined by the constraints as shown in the figure below in figure fig.3.4

Suppose that in addition to the existing constraints, the company is contracted to produce at least $30$ units each week. This additional constraint can be written as : $x+2y\ge 30$. As a boundary solution, the constraint would be: $x+y=30,(x=0,y=30)(x=30,y=0)$. the three structural constraints are shown in the figure in fig. 3.5.

This case presents the manager with demands which cannot simultaneously be satisfied