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

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Let Z=3x+9y....(1)

Converting inequalities to equalities

x + 3y = 60

x060
y200

Points are (0,20),(60,0)

x+y=10

x010
y100

Points are (0,10),(10,0)

x - y = 0

x01020
y01020

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.

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