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Unformatted text preview: Mahon, Kevin – Homework 12 – Due: Nov 17 2005, 3:00 am – Inst: Edward Odell 1 This printout should have 19 questions. Multiplechoice 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 14 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 = $18 correct 2. r max = $22 3. r max = $20 4. none of these 5. r max = $16 Explanation: Let r be the daily rate of renting a trailer. Then the number of trailers rented daily is 14 ( r 8) 2 . Hence the daily income, I ( r ), of the agency is given by I ( r ) = r µ 14 ( r 8) 2 ¶ . The income will be maximized, therefore, at the critical points of I ( r ). Now after differen tiation, I ( r ) = µ 14 ( r 8) 2 ¶ r 2 . Thus the critical points of I ( r ) occur at µ 14 ( r 8) 2 ¶ r 2 = 0 , i.e., r = 18 . Consequently, r max = $18 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 $520 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 = $75 2. none of these 3. rebate = $80 4. rebate = $70 5. rebate = $60 correct 6. rebate = $65 Explanation: Let $20 x be the rebate offered to a buyer. Then the price of a TV will be $(520 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 ) = (520 20 x )(100 + 5 x ) = 100(26 x )(20 + x ) = 100(520 + 6 x x 2 ) . But then R ( x ) = 100(6 2 x ) , while R 00 ( x ) = 100 × 2 < . Mahon, Kevin – Homework 12 – Due: Nov 17 2005, 3:00 am – Inst: Edward Odell 2 Consequently, the Revenue is maximized at x = 3, in which case the rebate = $60 . keywords: Stewart5e, 003 (part 1 of 1) 10 points A high speed office copier has an initial price of $5000. A service contract cost $240 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 ) = 5000 + 190 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 = 13 years 2. replacement time = 11 years 3. replacement time = 12 years 4. replacement time = 9 years 5. replacement time = 10 years correct Explanation: The average cost c ( x ) = C ( x ) x = 5000 + 190 x + 50 x 2 x = 5000 x + 190 + 50 x....
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This homework help was uploaded on 04/15/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.
 Fall '08
 schultz
 Differential Calculus

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