Question

The Profit P(x) due to advertising x,
in hundreds of rupees is given by
P(x) = 120 + 80 x-x², what amount of the
advertising fetches max profit and
the max profit ?
​

Answer 1

4000 Rs. of advertising fetches max profit

The max profit is 1480000 Rs.

Step-by-step explanation:

Given the variance of proft with rate x as

$P(x)=120+80x-x^2$

$\implies P(x)=-(x^2-80x-120)$

$\implies P(x)=-(x^2-2\times 40x+1600)+1600-120$

$\implies P(x)=-(x^2-2\times 40x+40^2)+1600-120$

$\implies P(x)=1480-(x-40)^2$

P(x) will be maximum when x = 40

Therefore, the amount 40 hundred rupees i.e. 4000 Rs.

Putting x = 40

We get

$P(x)=1480$ Hundred Rs.

Therefore, the maximum profit amount is 1480000 Rs.

Hope this answer is helpful.

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