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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 .

Respuesta :

Answer:

x=495

,P=241,525

Step-by-step explanation:

Given that

Profit=Total revenue - total cost

P= R -C

Also given that

[tex]R(x)=1000x-x^2[/tex]

[tex]C(x)=3400+10x[/tex]

So

[tex]P=1000x-x^2-3400-10x[/tex]

[tex]P=990x-x^2-3400[/tex]

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

[tex]\dfrac{dP}{dx}=990-2x[/tex]

⇒x=495

So total profit at x=445  ,P=241,525

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