A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture m order to maximise the profit?

Explanation

Let the number of souvenirs of type A be `x`
and the number of souvenirs of type B be `y`



Cutting
Type A requires`to`5 min
Type B requires`to`8 min
Maximum Time `to` 200 min
`therefore`
`5x+8y<=200`

Assembling
Type A requires`to`10 min
Type B requires`to`8 min
Maximum Time `to` 240 min
`therefore`
`10x+8y<=240`

Also, `x>=0,y>=0`

As, we need to maximize the profit, so function used here will be Maximize `Z`

Profit on Type A `to` Rs 5
Profit on Type B `to` Rs 6
`therefore` Maximize `Z=5x+6y`

Combining all constraints :
`Z=5x+6y`

Subject to Constraints:
`5x+8y<=200`
`10x+8y<=240`
`x>=0,y>=0`







Hence,
Profit will be maximum if company produces,

` " " " ` `8` souvenirs of type A
` " " " ` and `20` souvenirs of type B

Max. Profit = Rs 160