Question

Maximize Z = 3x + 9y Subject to the constraints: x + 3y ≤ 60 x + y ≥ 10 x ≤ y x ≥ 0, y ≥ 0

Answer 1

Let Z=3x+9y....(1)

Converting inequalities to equalities

x + 3y = 60

x	0	60
y	20	0

Points are (0,20),(60,0)

x+y=10

x	0	10
y	10	0

Points are (0,10),(10,0)

x - y = 0

x	0	10	20
y	0	10	20

Points are (0,0),(10,10),(20,20)

Plot the graph for the set of points

The graph shows the bounded feasible region. ABCD, with corner points A=(10,0),B=(5,5),C=(15,15) and D=(0,20)

To find maximum and minimum

Corner point Z = 3x + 9y

A = (0,10) 90

B = (5,5) 60

C = (15,15) 180

D = (0,20) 180

From the graph maximum value of X occurs at two corner points C(15,5) and D(0,20) with value 180 and minimum occurs at point B(5,5) with value 60.