Question

Two tailors, A and B, earn ₹300 and ₹400 per day respectively. A can stitch 6 shirts and 4 pair of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. How many days should each of them work if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labor cost?

Answer 1

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