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?

Question

Philoid · Accepted Answer

Let the total number of days tailor A work be x and tailor B be y.

∴According to the question,

6x + 10 y , 4x + 4y

Minimize Z = 300x + 400y

The feasible region determined by 6x + 10 y , 4x + 4y is 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

_{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.}