) The owner of a small shop selling hand made teddy bears has found that shouldn’t sell a running shoe for more than $50. Use your calculator to determine the price that maximizes profit. Write down: 10the number of teddy bears sold at price of xdollars is modeled by the function: ( )xxD4116−=Round off numerical answers in (c) and (d) to two decimal places. (a)Write down a model for( )xR, the revenue (in dollars) as a function of price. (b)When the price of a teddy bear is $15, what is the marginal revenue? (c)If each teddy bear costs the owner $7, and the owner has no other costs for selling the teddy bears, write down a model for ( )xP, the profit (in dollars) as a function of price. (d)Find the price to maximize the owner’s profit and what is the maximum profit? You must use calculus to show that your answer gives the maximum profit.
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11. (4 points) Find()the specific antiderivative of the function,F x( )f x, where Show all your work especially any equations you solve.
F
12. Let be the rate of change in the number of international calls billed in the US between 1980 and 2000 can be described by )(xPxexP1826.0432.32)(=million calls per year where xis the number of years since 1980. (a)(3 points) Evaluate 155)(dxxP(b) (2 points)Interpret your answer from part (a). 13. (5 points) Make a careful sketch of the region whose area is given by the definite integral: . Label the boundry curves, lines and corner points of the region. Then shade the region. ∫−4)8(2dxxxb) Estimate the area of the region using the 4 left rectangle approximation. Show all work and give exact answer.
∫
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