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sec43notes - MATH 119 Chapter 4 Derivative Applications...

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1 MATH 119 Chapter 4: Derivative Applications Class Note Ex 1: Read example 3 and 4 on page 191. Ex 2: An appliance firm determines to sell q radios, the price per radio is given by p = 300 - q it also determines that the total cost of producing q radios is given by: C(q) = 1000 + 0.5 q 2 . a) find the total revenue function b) find the total profit function ( P = R - C ) c) how many radios must be produced and sell to maximize the profit d) what is the maximum profit? (When P ' = 0 or when R ' = C ' as in section 2.6) e) what is the price per radio must be charged to maximize the profit? Ans: a) R = 300q - q 2 . b) P = -1.5q 2 + 300q -1000. c) 100. d) 14000 e) 200. Ex 3: A theater determine that if the admission price is $ 10, it averages 100 people in attendance. But for every increase of $ 2, it loses 5 customers from the average number. Every customers spends an average of $ 2 on concessions. What admission price should the theater charge in order to maximize the revenue? Solution: Revenue from tickets = (New Price) (New # of tickets) = (10 + 2 x ) (100 - 5 x ) Revenue from concessions = $ 2 (New # of customers)
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