Question

Total profit P is the difference between total revenue R and total cost C. Given the following​ total-revenue and​ total-cost functions, find the total​ profit, the maximum value of the total​ profit, and the value of x at which it occurs. R(x)= 1000x-(x squared) C(x)= 3400+10x .

Answer 1

Answer:

x=495

,P=241,525

Step-by-step explanation:

Given that

Profit=Total revenue - total cost

P= R -C

Also given that

$R(x)=1000x-x^2$

$C(x)=3400+10x$

So

$P=1000x-x^2-3400-10x$

$P=990x-x^2-3400$

Above equation is the total profit in terms if x.

Now to find maximum value of P we have to differentiate above equation with respect to x

So

$\dfrac{dP}{dx}=990-2x$

⇒x=495

So total profit at x=445  ,P=241,525