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

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

Philoid · Accepted Answer

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. The values of Z at the following points is

The minimum value of Z is at point C.

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