Question

You are thinking of opening a small copy shop. It costs $5000 to rent a copier for a year, and it costs $0.03 per copy to operate the copier. Other fixed costs of running the store will amount to $400 per month. You plan to charge an average of $0.10 per copy, and the store will be open 365 days per year. Each copier can make up to 100,000 copies per year.

Required:
a. For one to five copiers rented and daily demands of 500, 1000, 1500, and 2000 copies per day, find annual profit. That is, find annual profit for each of these combinations of copiers rented and daily demand.
b. If you rent three copiers, what daily demand for copies will allow you to break even?
c. Graph profit as a function of the number of copiers for a daily demand of 500 copies; for a daily demand of 2000 copies. Interpret your graphs.

Answer 1

Answer and explanation:

A. To calculate annual profit, we find:

Total income - total cost for the 365 days in a year

Total income for different daily demands:

For 500 copies= 500×365×0.10=$18250

For 1000 copies= 1000×365×0.10=$36500

For 1500 copies=1500×365×0.10=$54750

For 2000 copies=2000×365×0.10=$73000

Total cost using five copiers= 400×12+5000×5+500000×0.03= $44800

Total cost using four copiers=

400×12+5000×5+400000×0.03=

$36800

Annual profit with daily demand of 2000 and five copiers available= $73000-$44800= $28200

B.