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A manufacturer makes two types, A and B ...

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

Each mahine is available for amaximum 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 teaport of type A and 30 of type B should be manufacured in a day to get the maximum profit.

Text Solution

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Let x teaports of type A and y teapots of type B be manufactured. Then,
`x ge0,yge0,12x+6yle6xx60,18x+0yle6xx60,6x+9yle6xx60`
`impliesx ge0,yge0,2x+y le60,xle20,2x+3yle120.`
Profit function is `Z=(75)/(100)x +(50)/(100)y impliesZ=3/4x+1/2y.`
Maximize Z, subject to the constraints
`xge0,y ge0, xle20,2x+y le60,2x+3yle120.`
Then `x=15 and y=30` will give the maximum vallue of Z.
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