Question

Solve the following LPP graphically :

Maximize z = 5x + 3y

subject to 3x + 5y ≤ 15

5x + 2y ≤ 10

x,y ≥ 0

Answer 1

3x + 5y ≤ 15 ...(i)

3x + 5y = 15

5y = 15 - 3x

y = (15 - 3x)/5

x	0	5	-5
y	3	0	6

5x + 2y ≤ 10 ...(ii)

5x + 2y = 10

2y = 10 - 5x

y = (10 - 5x)/2

x	2	4	0
y	0	-5	5

Feasible solution

= (2,0),(20/19,45/19),(0,3) at (2,0)

z = 5x + 3y = 5 x 2 + 3 x 0 at (20/19,45/19)

z = 5x + 3y = 5 x (20/19) + 3 x (45/19) = ((100/19) + (135/19)) = 235/19 

= 12.37

at (0,3)

z = 5x + 3y = 5 x 0 + 3 x 3 = 9

z_max = 235/19