Question

Consider a mail-order (only) catalog company that traditionally sends large holiday catalogs to four million past and one million potential customers. This is an expensive process, as the printing and mailing costs $3 for each catalog, and typically only 6% of existing customers and 2% of potential customers make a purchase. The average sale to an existing customer nets the company $30 in profit (i.e., after all expenses), while the average sale to a new customer nets the company $25 in profit. Delivery of a catalog without a sale will result, of course, in an expense.

Answer 1

past customer = 4 million = 4,000,000

potential customers = 1 million = 1,000,000

profit from past customers = (no. off purchases)*(net profit from purchase) - (no. of non purchases)*(expense)

average profit from past customers = (6% * 4,000,000)*30 - ((1 - 6%)*4,000,000)*(3) dollars = -4080000 dollars

profit from potential customers = (no. off purchases)*(net profit from purchase) - (no. of non purchases)*(expense)

average profit from past customers = (2% * 1,000,000)*25 - ((1 - 2%)*1,000,000)*(3) dollars = -2440000 dollars

average total profit = average profit from past customers + average profit from past customers

= (-4080000) + (-2440000) dollars

average total profit = -6520000 dollars

P.S. (please upvote if you find the answer satisfactory)