Question

Find the minimum value of Z = 3x + 5y, subject to the constraints

 - 2x + y ≤ 4, x + y ≥ 3, x - 2y ≤ 2, x ≥ 0 and y ≥ 0

Answer 1

The feasible region determined by the - 2x + y ≤ 4, x + y ≥ 3, x - 2y ≤ 2, x ≥ 0 and y ≥ 0 is given by

Here the feasible region is unbounded. The vertices of the region are A(0,4) ,B(0,3) ,C \((\frac{8}{3},\frac{1}{3})\). 

The values of Z at the following points is

The minimum value of Z is \(\frac{29}{3}\) at point C \((\frac{8}{3},\frac{1}{3})\).