Question

Solve the following problem graphically: Minimise and Maximise Z = 3x + 9y subject to the constraints: x + 3y ≤ 60 x + y ≥ 10 x ≤ y x ≥ 0, y ≥ 0

Answer 1

Maximize Z = 3x + 9y

Minimize Z = 3x + 9y

subject to the constraints

x + 3y ≤ 60

x + y ≥ 10

x ≤ y

x ≥ 0, y ≥ 0

First we graph all these equation on the graph:

Therefore, DABC is the feasible region, which is bounded by corner point (5,5) (0,10), (0, 20) and (15,15)

At (5,5) Z = 15 + 45 =60

at ( 0,10) Z = 0 +90 = 90

at ( 0,20) Z = 0+180 =180

at (15,15) Z = 45 + 135 = 180

Minimum value 60 at (5,5)[ Z is minimum at (5,5) ]

Maximum value 180 at (0,20) and (15,15) [Z is maximum at (0,20) and (15,15)]