course mth 271 è²æªLãÙÀ•Æ“l¬|îúGó™Ú½åyÍ꯯assignment #015 015. `query 15 Applied Calculus I 11-06-2007
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10:30:27 2.3.32 P=22t^2+52t+10000, t from 1970; find P at t=0,10,20,25 and explain; find dP/dt; evaluate at given t and explain your results.
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RESPONSE --> this problem wasnt assigned but... (0,10000) (10,12720) (15,15730) (20,19840) (25,25056) p'=44t+52 (0,52) (10,492) (15,712) (20,932) (25,1152) p' is the rate of change of pop wrt time t confidence assessment: 3
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10:30:38 dP/dt=44t + 52 (power function rule on each nonconstant term) When t = 0, 10, 20 and 25 you would have P = 10,000, 12,700, 20,000, 25,000 approx. At these values of t we have dP / dt = 52, 492, 932 and 1152 (these are my mental calculations--check them). dP / dt is the rate of change of the population with respect to time t **
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RESPONSE --> yup self critique assessment: 3
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10:35:22 2.3.48 demand fn p = 50/`sqrt(x), cost .5x+500. Find marginal profit for x=900,1600,2500,3600 Explain how you found the marginal profit, and give your results.
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RESPONSE --> how do you get the deriv of 50/sq root x? confidence assessment: 0
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10:40:27 x represents the number of items sold. If x items are sold at price p = 50 / `sqrt(x), then revenue is price of item * number sold = 50 / `sqrt(x) * x = 50 `sqrt(x). The profit is revenue - cost = 50 `sqrt(x) - .5 x - 500. The marginal profit is the derivative of the profit function, which is (50 `sqrt(x) - .5 x - 500 ) ' = 25 / `sqrt(x) - .5. Evaluating the marginal profit at x = 900, 1600, 2500 and 3600 we get values .33..., .125, 0 and -.0833... . This shows us that the marginal profit, which is the limiting value of the increase in profit per additional item manufactured, is positive until x = 2500. This means that it is to the advantage of the producer to produce new items when x = 900 and when x = 1600, but that the advantage disappears as soon as x reaches 2500. So 2500 is the best selling price. When x = 3600 production of additional items reduces profits. **
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RESPONSE --> i wish you worked out all of the steps in finding the deriv b/c sometimes it is hard to follow how you are getting the answers self critique assessment: 3
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