Question

Solve the following L.P.P. graphically Minimize Z = 3x + 5y Subject to 2x + 3y ≥ 12 
-x + y ≤ 3 
x ≤ 4 
y ≥ 3 

Answer 1

Inequation	Equation	Points on line
2x + 3y ≥12	2x + 3y = 12	(0,4),(6, 0)
- x + y ≤ 3	- x+ y = 3	(0,3), (-3,0)
x ≤ 4	x = 4
y ≥ 3	y = 3

Requjred region is bounded region ABCDA Co-ordinates of corner points are 

A = (1,5,3) B = (4, 3) 

C = (4, 7) D = (0.6, 3.6) 

Corner points Z = 3x + 5y 

At A(1 ,5, 3)  Z = 3 (1.5) + 5 (3) 
                        = 4.5 + 15 = 19.5

At B(4. 3)     Z = 3(4) + 5(3)
                       = 12 + 15 = 27

At C(4, 7)    Z = 3 (4 ) + 5 (7) 
                     =  12 + 35 = 47 

At D(0.6, 3.6)  Z = 3 (0.6) + 5 (3.6)
                         = ·1.8 + 18 = 19.8 

From the above data ·
Minimum value of Z is 19.5 at point A ( 1.5, 3)
Solution of L.P.P. is X = 1.5, Y = 3, `Z_min` = 19.5