Question

Find the maximum and minimum values of Z = 2x + y, subject to the constraints 

X + 3y ≥ 6, x - 3y ≤ 3, 3x + 4y ≤ 24, 

- 3x + 2y ≤ 6, 5x + y ≥ 5, x ≥ 0 and y ≥ 0.

Answer 1

The feasible region determined by X + 3y ≥ 6, x - 3y ≤ 3, 3x + 4y ≤ 24, - 3x + 2y ≤ 6, 5x + y ≥ 5, x ≥ 0 and y ≥ 0 is given by

The corner points of the feasible region are A(4/3,5) , B(4/13,45/13), C(9/14,25/14) , D(9/2,1/2) , E(84/13,15/13).

The value of Z at corner points are

The maximum and minimum value of Z is 183/13 and 43/14 at points E(84/13,15/13) and C(9/14,25/14).