An importer of Brazilian coffee estimates that local consumers will buy approxim

Question

An importer of Brazilian coffee estimates that local consumers will buy approximately D(p)=rac{4424}{p^2} pounds of the coffee per week when the price is p dollars per pound. It is also estimated that t weeks from now, the price of Brazilian coffee will be p(t)=0.02 t^2+ 0.1 t+ 6 dollars per pound. a) At what rate will the demand for coffee be changing with respect to price when the price is 10 dollars? b) At what rate will the demand for coffee be changing with respect to time 10 weeks from now? c) Is the demand increasing after 10 weeks? Answer (Y/N):

Explanation / Answer

dD/dp = -2*4742/p^3 so when p=9 dD/dp = -2*4742/9^3 = -13 pound/$ dD/dt = dD/dp dp/dt = -2*4742/p^3 (0.04t +.01). In 10 weeks, p=2+0.1+6=8.1 so dD/dt =-2*4742/8.1^3 (0.41) = -7.32 pound/week

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