Quantitative Business Methods Hw 2

MA 218 Classwork 2/3 1. Rafael estimates that it costs $14 to produce a calculator that sells for $23. His

factory has fixed costs of $1200. Let q be the number of calculators he produces

and sells.

a) Find a function C(q) that outputs the cost of selling q calculators. Explain.

b) Find a function R(q) that outputs the revenue from selling q calculators.

Explain.

c) Find a function P(q) that outputs the profit from selling q calculators. Explain.

d) Carefully graph all three functions on the same xy-plane. Explain how C(q), R(q)

and P(q) are related. What does the intersection point of R(q) and C(q) represent?

Explain.

e) How much profit is made when 100 calculators are sold? How much when 2000

calculators are sold? Explain.

2. In 2012, there was a spike in the price of beef. In their public financial

disclosure report​[1]​ for that year, McDonalds stated that the average franchise profited 39 cents for every regular sized clutch of French fries sold, 96 cents for

every medium beverage sold, and lost 6 cents for every Double Quarter Pounder

with Cheese​TM​ sold.

a) Write a function that outputs the profit from those three items in dollars. (Hint:

let x be fries, y be drinks and z be burgers. Your function should have all three

variables.) Explain

b) Say that Bob’s McDonalds franchise sells 500 of these burgers in a day. Write a

new daily profit function that reflects this information.

c) Now say in addition that Bob needs to make 650 dollars per day on these three

items for him to stay in business. How many drinks must he sell to make this daily

profit? [Hint: The answer depends on x, the number of fries. Plug in the important

information and use algebra to produce an inequality with just y on one side.]

d) Make a graph of the situation in part c), with fries on the horizontal axis and

drinks on the vertical axis. Shade in a ‘region of profitability’ on your graph.

Explain.

e) McDonalds has been in business a long time and generally has been very

profitable. Explain why you think that they would be willing to lose money selling

certain hamburgers. Given your analysis above, if you owned a franchise, how

would you would use your work above to maximize your profits.

[1] Source: 2012 Fidelity Dow Jones Public Disclosure Sheet

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