Q. 20

# A manufacture makes two types, A and B, of teapots. Three machines are needed for the manufacture and the time required for each teapot on the machines is given below.

Each machine is available for a maximum of 6 hours per day. If the profit on each teapot of type A is 75 paise and that on each teapot of type B is 50 paise, show that 15 teapots of type A and 30 of type B should be manufactured in a day to get the maximum profit.

Answer :

Let x teapots of type A and y teapots of type B manufactured.

Then,

x ≥ 0, y ≥ 0

Also,

12x + 6y ≤ 6 × 60

12x + 6y ≤ 360

2x + y ≤ 60…..(1)

And,

18x + 0y ≤ 6 × 60

X ≤ 20……(2)

Also,

6x + 9y ≤ 6 × 60

2x + 3y ≤ 120…..(3)

The profit will be given by: Z

On plotting the constraints, we get,

Profit will be maximum when x = 30 and y = 15

Hence, Proved.

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PREVIOUSA small firm manufactures gold rings and chains. The combined number of rings and chains manufactured per day is at most 24. It takes 1 hour to make a ring and half an hour for a chain. The maximum number of hour to available per day is 16. If the profit on a ring is ₹300 and that on a chain is ₹190, how many of each should be manufactured daily so as to maximize the profit?NEXTA manufacture makes two types, A and B, of teapots. Three machines are needed for the manufacture and the time required for each teapot on the machines is given below.Each machine is available for a maximum of 6 hours per day. If the profit on each teapot of type A is 75 paise and that on each teapot of type B is 50 paise, show that 15 teapots of type A and 30 of type B should be manufactured in a day to get the maximum profit.

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