two tailors A and B earn Rs. 300 and Rs. 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. how many days should each of them work to produce at least 60 shirts and 32 trousers at a minimum labour cost?
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Hey !!
Shirts Trousers Payment per day
(x) A 6 4 Rupees 300
(x) B 10 4 Rupees 400
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60 32
Let A work for x and B for y days
Constraints : z = 300 x + 400 y
4x + 4y ≥ 32
x ≥ 0
y ≥ 0
PQR is the solution
P (3,3) z = 300 (s) + 400 (s) = Rupees 2700
Q (0,8) z = 400 (8) = Rupees 3200
R (10,0) z = 300 (10) = Rupees 3000
Hence, z is minimum when A works for 5 days and B works for 3 days.
GOOD LUCK !!
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