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12. The profit of a​ company, in​ dollars, is the difference between the​ company's revenue and cost. The​ cost, C(x), and​ revenue, R(x), are functions for a particular company. The x represents the number of items produced and sold to distributors.

C(x)=2300+60x

R(x)=820x−x2

12 The profit of a company in dollars is the difference between the companys revenue and cost The cost Cx and revenue Rx are functions for a particular company class=

Respuesta :

devishri1977

Answer:

$ 142100

Step-by-step explanation:

Profit is the difference between the revenue and the cost

        P(x) = R(x) - C(x)

                = 820x - x² - (2300 + 60x)

                = 820x - x² - 2300 - 60x

                = -x² + 820x - 60x - 2300

         P(x) = -x² + 760x - 2300

We can find the maximum profit of the company by finding the maximum of the parabolic function.

a =  -1   ; b = 760  and c = -2300

       [tex]\sf \boxed{P_{max} = c - \dfrac{b^2}{4a}}[/tex]

                  [tex]\sf = -2300 - \dfrac{760^{2}}{4*(-1)}[/tex]

                  [tex]\sf = -2300 +\dfrac{577600}{4}\\\\ = -2300 + 144400\\= 142100[/tex]

[tex]\sf \boxed{P_{max}= \$ 142100}[/tex]

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