Question

Solve the following Linear Programming Problem graphically: Maximise Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.

Answer 1

To solve the given LPP graphically

1) Draw all given lines,by equating to RHS

x+2y=10

put x= 0,y = 5

put y= 0 x = 10

Draw a line to meet the points (0,5) (10,0)

by the same way the other line is to be drawn

Please refer attachment for the common reason bounded by all constraints.

Now to,

Maximise Z = 3x + 2y

Put the coordinates of A,B,C and D

A(0,0)=> Z = 3(0)+2(0)=0

E(4,3)=> Z= 3(4)+2(3)=18

C(0,5)=> Z=3(0)+2(5)=10

D(5,0)=> Z= 3(5)+2(0)=15

So,the function get Maximum value at

x=4 and y = 3

Hope it helps you.