Q. 1

# Two tailors, A and B earn ₹ 300 and ₹ 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. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.**[CBSE 2017]**

**[CBSE 2017]**

Answer :

Let A works for x days and B works for y days.

∴ x ≥ 0, y ≥ 0

Minimum no. of shirts = 60

**Given:**A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers

∴ 6x + 10y ≥ 60

3x + 5y ≥ 30

Minimum no. of trousers = 32

∴ 4x + 4y ≥ 32

x + y ≥ 8

Let z be the total labor cost.

∴ z = 300x + 400 y

∴ the given L.P problem reduces to: z = 300x + 400y

x ≥ 0, y ≥ 0, 3x + 5y ≥ 30, x + y ≥ 8

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