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) 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. 7
11. (4 points) Find()the specific antiderivative of the function,F x( )f x, where Show all your work especially any equations you solve. F12. 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. ∫28