Web Site Profit You operate a gaming Web site, www .mudbeast.net, where users must pay a small fee to log on. When you charged $2 the demand was 280 log-ons per month. When you lowered the price to $1.50, the demand increased to 560 logons per month.
a. Construct a linear demand function for your Web site and hence obtain the monthly revenue R as a function of the log-on fee x.
b. Your Internet provider charges you a monthly fee of $30 to maintain your site. Express your monthly profit P as a function of the log-on fee x, and hence determine the logon fee you should charge to obtain the largest possible monthly profit. What is the largest possible monthly profit? HINT [See Example 4.]
Example 4:
As the operator of YSport Fitness gym, you calculate your demand equation to be
q = −0.06p + 84
where q is the number of members in the club and p is the annual membership fee you charge.
a. Your annual operating costs are a fixed cost of $20,000 per year plus a variable cost of $20 per member. Find the annual revenue and profit as functions of the membership price p.
b. At what price should you set the annual membership fee to obtain the maximum revenue? What is the maximum possible revenue?
c. At what price should you set the annual membership fee to obtain the maximum profit? What is the maximum possible profit? What is the corresponding revenue?
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