Question

Solve the following problem graphically: Minimise and Maximise = 2 + 6
Subject to the constraints: + 2 ≤ 10, + ≤ 7, ≥ 2, ≥ 0, ≥ 0

Answer 1

Answer:

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.

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