BUSINESS CALCULUS 1 - EXAM 1 - Take home part - due Feb. 24 at 9:00am Name Score Directions: You must show work. Partial or full credit will only be given if answers are supported by work. Also, if you have the correct answer but incorrect work to support the answer you will not receive full credit. 1. A company's total sales (in millions of dollars} t months from now are given by em = 3 + Jr (5 pts) a. Find the instantaneous rate of change of sales with respect to time. b. Find S'(25) with the correct units and then write an interpretation of the result. 2. A company manufactures fuel tanks for cars. The total weekly cost. (30:) (in dollars) of producing x tanks is given by 00:} = 20000 + 100): 004x? (6 m5) at. Find the exact cost of producing the 61St fuel tank. b. Find the marginal cost at a production level of 60 tanks per week and compare your answer to your result in part a. A company is planning to manufacture and sell hair dryers. The price-demand and cost equations are estimated to be respectively; MK) = 50 0.2x. 000 = 5x + 1700 where x is the # of hair dryers that can be sold at a price of $p per hair dryer and cm is the total cost (in dollars} of producing x dryers. (19 pts} Find the revenue equation. Graph the cost and revenue functions on the same coordinate system. {Do this as l instructed in class.) c. Find the break-even points and indicate on the graph the regions of loss and profit. d Find the profit equation. 9. Find the marginal profit at x = 150, include the correct units, and write an interpretation of the result. as