Question

The total cost of producing `x` radio sets per day is `R sdot((x^2)/4 35 x+25)` and the price per set at which they may be sold is `R sdot(50-x/2)dot` Find the daily output to maximize the total profit.

Answer 1

Here, total cost of `x` radios ` = x^2/4+35x+25` Rs
Selling price of `x` radios ` = x(50-x/2) = 50x-x^2/2` Rs
`:.` Profit `(P)= 50x-x^2/2 - (x^2/4+35x+25)` Rs
`=> P = -3/4x^2 + 15x -25`
`=>(dP)/dx = -3/2x + 15`
For, maximum profit, `(dP)/dx` should be `0`.
`=> -3/2x + 15 = 0`
`=> x = 10`
So, to maximize the total profit, `x` should be `10`.