A furniture manufacturing company recently completed some market research and have determined they can model the price/demand for a new line of couches with the following: p = 3750 − 0.25q where p is the retail price of the couch and q are the number of couches demanded.
(a) [2 points] What is the revenue as a function of number of couches sold?
(a)
(b) [2 points] The fixed costs associated with retooling the manufacturing plant is $500,000 and once the factory is operational, each couch will cost incur an ad- ditional $425 to make. Based on this information, what is the cost as a function of the number of couches manufactured?
(b)
(c) [2 points] If the number of couches sold is exactly the number of couches manufac- tured, what is the profit as a function of the number of couches sold?
(c)
(d) [2 points] What are the break-even points for the profit (reminder: break-even means the profit is exactly $0). Round to the nearest whole number.
(d)

Math 112 Page 5 of 5 Written Homework 8
Question 4 cont’d
(e) [1 point] How many couches should be manufactured/sold in order to maximize profit? Round to the nearest whole number.
(e)
(f) [1 point] How much profit can the company anticipate if they maximize their profit? Round to the nearest million dollars