8 W4 points T The latest demand equation for your gaming website, www.mudbeast.n

Question

8 W4 points T The latest demand equation for your gaming website, www.mudbeast.net, is given by q=-200x + 1100 where q is the number of users who log on per month and x is the log-on fee you charge. Your Internet provider bills you as follows: Site maintenance fee $50 per month High-volume access fee: $0.40 per log-on Find the monthly cost as a function of the log-on fee x. C(x) Find the monthly profit as a function of x. Determine the log-on fee you should charge to obtain the largest possible monthly profit. x per log-on What is the largest possible monthly profit? Need Help?ReadtWatch It Submit Answer Save Progress Practice Another Version

Explanation / Answer

fixed cost = $ 50 / month

variable cost = $ .40

hence ,

C(x) = .40q + 50

C(x) = .40 ( - 200x + 1100 ) + 50

C(x) = -80x + 490

R(x) = xq

= x( - 200x + 1100 )

= -200x^2 + 1100 x

P(x) = R(x) - C(x)

= -200x^2 + 1100 x + 80x - 490

P(x) = - 200x^2 + 1180 x - 490

x max = - b / 2a

= -1180 / 2(-200)

= $ 2.95

largest possible monthly profit is

- 200(2.95)^2 + 1180 (2.95) - 490

$ 1250.5

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