Question

Solve the following Linear Programming Problem graphically: Minimise Z = - 3x + 4 y subject to x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.

Answer 1

To solve the given LPP graphically

1) Draw all given lines,by equating to RHS

x+2y = 8

put x= 0,y = 4

put y= 0 x = 8

Draw a line to meet the points (0,4) (8,0)

by the same way the other line

Please refer attachment for the common reason bounded by all constraints(The darkest region is the common region)

Now to Minimise


Z = - 3x + 4 y

Put the coordinates of A,B,C and D

A(4,0)=> Z = -3(4)+4(0)=-12

B(2,3)=> Z= -3(2)+4(3)=6

C(0,0)=> Z=-3(0)+4(0)=0

D(0,4)=> Z= -3(0)+4(4)=16


So,the function get Minimum at x =4 and y = 0

Hope it helps you.