Q11 of 97 Page 1376

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?


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.


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