Question

Solve the linear programming problem by the method of corners.

Maximize	P = 5x + 6y
subject to	x	+	y	≤	10
	3x	+	y	≥	12
	−2x	+	3y	≥	8
	x ≥ 0, y ≥ 0

Answer 1

the first constraint is

divide by 10

compare with the line  

so here x-intercept is

and the y-intercept is

draw a line between (10,0), and (0,10)

.

.

the second constraint is

divide by 12

compare with the line  

so here x-intercept is

and the y-intercept is

draw a line between (4,0), and (0,12)

.

.

the third constraint is

divide by 8

compare with the line  

so here x-intercept is

and the y-intercept is

draw a line between (-4,0), and (0,2.66)

.

from the graph, corner points are

(1,9), (2.55,4.36), (4.4,5.6)

The value of the objective function at each of these extreme points is as follows:

Extreme Point Coordinates (x,y)	Objective function value P=5x+6y
A(1,9)	5(1)+6(9)=59
B(2.55,4.36)	5(2.55)+6(4.36)=38.91
C(4.4,5.6)	5(4.4)+6(5.6)=55.6

The maximum value of the objective function z=59 occurs at the extreme point (1,9).

Hence, the optimal solution to the given LP problem is x=1,y=9 and max z=59.

.