hw12 - Granillo, Yvette Homework 12 Due: Nov 17 2005, 3:00...

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Unformatted text preview: Granillo, Yvette Homework 12 Due: Nov 17 2005, 3:00 am Inst: Edward Odell 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A trailer rental agency rents 10 trailers per day at a rate of $8 per day. It discovers that for each $2 increase in rate, one fewer trailer is rented. Determine the rate, r max , which maximizes the rental income. 1. r max = $14 correct 2. r max = $16 3. none of these 4. r max = $18 5. r max = $12 Explanation: Let r be the daily rate of renting a trailer. Then the number of trailers rented daily is 10- ( r- 8) 2 . Hence the daily income, I ( r ), of the agency is given by I ( r ) = r 10- ( r- 8) 2 . The income will be maximized, therefore, at the critical points of I ( r ). Now after differen- tiation, I ( r ) = 10- ( r- 8) 2 - r 2 . Thus the critical points of I ( r ) occur at 10- ( r- 8) 2 - r 2 = 0 , i.e., r = 14 . Consequently, r max = $14 is the rate that maximizes income. keywords: Stewart5e, 002 (part 1 of 1) 10 points Circuit City has been selling 100 television sets a week at $600 each. A market survey indicates that for each $20 rebate offered to a buyer, the number of sets sold will increase by 5 per week. How large a rebate should Circuit City offer a buyer in order to maximize its revenue? 1. rebate = $115 2. rebate = $100 correct 3. rebate = $95 4. rebate = $110 5. rebate = $105 6. none of these Explanation: Let $20 x be the rebate offered to a buyer. Then the price of a TV will be $(600- 20 x ) and the number of sets sold at this price will be 100 + 5 x . The revenue with this rebate is thus R ( x ) = (600- 20 x )(100 + 5 x ) = 100(30- x )(20 + x ) = 100(600 + 10 x- x 2 ) . But then R ( x ) = 100(10- 2 x ) , while R 00 ( x ) =- 100 2 < . Granillo, Yvette Homework 12 Due: Nov 17 2005, 3:00 am Inst: Edward Odell 2 Consequently, the Revenue is maximized at x = 5, in which case the rebate = $100 . keywords: Stewart5e, 003 (part 1 of 1) 10 points A high speed office copier has an initial price of $3200. A service contract cost $260 for the first year and increases by $100 per year thereafter. It can be shown that over x years the total cost of the copier is given by C ( x ) = 3200 + 210 x + 50 x 2 . When is the average cost per year smallest? (This is often referred to as the replacement time for a piece of equipment.) 1. replacement time = 9 years 2. replacement time = 7 years 3. replacement time = 8 years correct 4. replacement time = 11 years 5. replacement time = 10 years Explanation: The average cost c ( x ) = C ( x ) x = 3200 + 210 x + 50 x 2 x = 3200 x + 210 + 50 x....
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This test prep was uploaded on 04/16/2008 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.

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hw12 - Granillo, Yvette Homework 12 Due: Nov 17 2005, 3:00...

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