Question

Solve the following LPP graphically:

Maximize Z = 9x + 13y subject to constraints

2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0

Solution: Convert the constraints into equations and find the intercept made by each one of it.

Inequation	Equation	X intercept	Y intercept	Region
2x + 3y ≤ 18	2x + 3y = 18	(9, 0)	(0, ___)	Towards origin
2x + y ≤ 10	2x + y = 10	( ___, 0)	(0, 10)	Towards origin
x ≥ 0, y ≥ 0	x = 0, y = 0	X axis	Y axis	______

The feasible region is OAPC, where O(0, 0), A(0, 6),

P( ___, ___ ), C(5, 0)

The optimal solution is in the following table:

Point	Coordinates	Z = 9x + 13y	Values	Remark
O	(0, 0)	9(0) + 13(0)	0
A	(0, 6)	9(0) + 13(6)	______
P	( ___,___ )	9( ___ ) + 13( ___ )	______	______
C	(5, 0)	9(5) + 13(0)	______

∴ Z is maximum at __( ___, ___ ) with the value ___.

Answer 1

Convert the constraints into equations and find the intercept made by each one of it.

Inequation	Equation	X intercept	Y intercept	Region
2x + 3y ≤ 18	2x + 3y = 18	(9, 0)	( 0, 6)	Towards origin
2x + y ≤ 10	2x + y = 10	(5, 0)	(0, 10)	Towards origin
x ≥ 0, y ≥ 0	x = 0, y = 0	X axis	Y axis	1st quadrant

The feasible region is OAPC, where O(0, 0), A(0, 6),

P(3, 4), C(5, 0)

The optimal solution is in the following table:

Point	Coordinates	Z = 9x + 13y	Values	Remark
O	(0, 0)	9(0) + 13(0)	0
A	(0, 6)	9(0) + 13(6)	78
P	(3, 4)	9(3) + 13(4)	79	maximum
C	(5, 0)	9(5) + 13(0)	45

∴ Z is maximum at P(3, 4) with the value 79.