Consider the following maximization problem Max z x1 2x2 s

Consider the following maximization problem:

Max z = x1 + 2x2

s.t. x1 + x2 300

2x1 + x2 400

2x1 + 5x2 750

x1, x2 0

Use graphical method. What is the optimal value of z? Choose the closest value.

562

712

734

720

Solution

Our objective is to maximise z = x1+2x2

The corner points are (100,200) (300,0) (250,50)(375,0)

z (100,200) = 500

z(300,0) = 300

z(250,50) = 350

z(375,0) = 375

Optimal value is 500 and closest is 562