Henrietta Fowler publishes Metropolitan Chicken, a magazine devoted to raising poultry in urban environments. She has conducted extensive surveys from potential readers and potential advertisers. The amount that advertisers are willing to pay for an ad in Metropolitan Chicken is proportional to the number of subscribers. She estimates that if she charges advertisers a rate of PA cents per-subscriber for each ad, she could attract QA = 80−PA advertisements. Suppose that the cost of printing and distributing an advertisement is negligible. The number of subscribers to Metropolitan Chicken is determined by the demand equation QS = 4, 000 − PS where PS is the subscription price measured in cents. The cost of printing, handling, and mailing a copy of Metropolitan Chicken is 400 cents per subscriber.
(a) Write an expression for Metropolitan Chicken’s total revenue from advertising as a function of the variables QA and QS. (Remember that total revenue is revenue per reader times the number of readers.) __________________ Solve for the number of ads and the price per-subscriber that maximizes her advertising revenue. _________________ Does this answer depend on the number of subscriptions sold? _____ How much extra advertising revenue (in cents) would Henrietta get if she added one more subscriber? __________
(b) Write an expression for Metropolitan Chicken’s net revenue (in cents) from subscriptions (total subscription revenue minus costs of printing, handling, and mailing to subscribers) as a function of QS. ______________ If Henrietta were to choose QS to maximize subscription revenue, how many subscriptions would she sell and at what price? ____________
(c) Write an expression for Henrietta’s total profit from advertising and subscriptions as a function of the two variables QA and QS. ___________ What quantities QA and QS should she choose in order to maximize profits? ________________