Rich and Betsy Cuik started a small business. They manufacture a microwavable coffee-to-go cup called Cuik Cuppa Coffee. It contains spring water and ground coffee beans in a tea-bag-like pouch. Each cup costs the company $1.00 to manufacture. The fixed costs for this product line are $1,500. Rich and Betsy have determined the demand function to be q = -1,000p + 8,500, where p is the price for each cup.
a. Write the expense equation in terms of the demand, q.
b. Express the expense equation found in part a in terms of the price, p.
c. Determine a viewing window on a graphing calculator for the expense function. Justify your answer.
d. Draw and label the graph of the expense function.
e. Write the revenue function in terms of the price.
f. Graph the revenue function in a suitable viewing window. What price will yield the maximum revenue? What is the revenue at that price? Round both answers to the nearest cent.
g. Graph the revenue and expense functions on the same coordinate plane. Identify the points of intersection using a graphing calculator. Round your answers to the nearest cent. Identify the price at the breakeven points.