Question

Consider the linear programming problem: Maximum z = 4x + y Subject to constraints: x + y < 50, 3x + y < 9x, y < 0 

(a) Draw the feasible region 

(b) Find the corner points of the feasible region 

(c) Find the corner at which ‘z’ attains its maximum value

Answer 1

(a) x + y = 50,

x	0	50
Y	50	0

3x + y = 90

x	0	30
Y	90	0

(b) Solving the equations we get the points as O(0, 0) A(30, 0); B(20, 30); C(0, 50)

(c)

Vertices	Z
0(0,0)	0
A(30,0)	120 maximum
B(20,30)	110
C(0,50)	50

Z attains maximum at A(30, 0)