The latest demand equation for your web site is given by q= -400x + 1200 where q

Question

The latest demand equation for your web site is given by q= -400x + 1200 where q is the number of users who log on/month and x is the logon fee you charge. Your internet provider bills you as follows: site maintenance fee $20/month high volume access fee 50 cents/log on Find the monthly cost as a function of the logon fee x. Find the monthly profit as a function of x and determine the logon fee you should charge to obtain the largest possible monthly profit. WHat is the largest possible monthly profit?

Explanation / Answer

monthly cost , c = 20 + 0.5*x monthly revenue, r = q*x monthly profit, p = qx - c = -400x^2 + 1200x - 20 - 0.5x = -400x^2 + 1199.5x - 20 dp/dx = -800x + 1199.5 = 0 x = 1.5 $ / logon largest profit, pmax = 879.25 $

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