# P05Ans - Price \$ 670 2 When a ﬁsh swims with velocity v...

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Project 5 MAC 2233 1. An apartment complex contains 50 one-bedroom apartments. Whern rent is set at \$ 550 per month, all the units will be occupied. Each \$ 30 increase in rent results in an average of two less units occupied. Each occupied unit requires an average of \$ 40 per month for service and repairs. a) Write an equation which expresses the relationship between the rental price p of one month and the number of units x occupied that month. b) Write functions that represent the total revenue R ( x ) and total cost C ( x ) for one month in terms of the number of units x occupied that month. c) Write a function that represents the total proﬁt P ( x ) for one month in terms of the num- ber of units x occupied that month. P ( x ) = 1260 x - 15 x 2 d) Quickly sketch the proﬁt function P ( x ) . What rental price and what number of occupied units seem to maximize proﬁt?
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Unformatted text preview: Price: \$ 670 2. When a ﬁsh swims with velocity v ft/sec against a current with velocity u ft/sec, the energy it expends per second is proportional to v 3 (it is kv 3 for some constant k ). Note that the net swimming velocity of the ﬁsh is v-u ft/sec. Suppose the current of a river is observed to be 5 ft/sec and k = 2 for a certain ﬁsh. Write a formula that expresses the total energy E expended by the ﬁsh as it travels a distance of 300 feet. See related problem in textbook 3. Packaging: A cylindrical tube, constructed of heavy cardboard with plastic ends, must hold a volume of 144 cubic feet. Express the cost of the tube as a function of radius r if cardboard is \$ 1 per square foot and plastic is \$ 3 per square foot? C ( r ) = 288 r + 6 πr 2...
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