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# hw12 - Granillo Yvette Homework 12 Due 3:00 am Inst Edward...

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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 0 ( 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 0 ( x ) = 100(10 - 2 x ) , while R 00 ( x ) = - 100 × 2 < 0 .

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Granillo, Yvette – Homework 12 – Due: Nov 17 2005, 3:00 am – Inst: Edward Odell 2 Consequently, the Revenue is maximized at x 0 = 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 . In practical terms it represents the total cost (initial cost plus maintenance costs) of the computer averaged out over an x year period. The marginal average cost, therefore, is given by c 0 ( t ) = - 3200 x 2 + 50 , and so the only critical point of c ( x ) for x > 0 is the positive solution of c 0 ( x ) = 0, i.e. , replacement time = r 3200 50 = 8 years . keywords: Stewart5e, 004 (part 1 of 2) 10 points The marketing department of a company has determined that the cost (in dollars) of producing x units of a new product is given by C ( x ) = 300 + 180 x, while the demand equation for that product will be given by p = 300 - 3 100 x.
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hw12 - Granillo Yvette Homework 12 Due 3:00 am Inst Edward...

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