Let the total number of days tailor A work be x and tailor B be y.
∴According to the question,
6x + 10 y ≥ 60, 4x + 4y ≥ 32, x ≥ 0, y ≥ 0
Minimize Z = 300x + 400y
The feasible region determined by 6x + 10 y ≥ 60, 4x + 4y ≥ 32, x ≥ 0, y ≥ 0is given by
The feasible region is unbounded. The corner points of feasible region are A(0,8),B(5,3),C(10,0) .
The value of Z at corner point is
Corner Point |
Z = 300x + 400y |
|
A(0, 8) |
3200 |
|
B(5, 3) |
2700 |
Minimum |
C(10, 0) |
3000 |
|
The minimum value of Z is 2700 at point (5,3).
∴Tailor A must work for 5 days and tailor B must work for 3 days for minimum expenses