In the 1930s a prominent economist devised the following demand function for cor

Question

In the 1930s a prominent economist devised the following demand function for corn: p = 6,600,000 q1.3 , where q is the number of bushels of corn that could be sold at p dollars per bushel in one year. Assume that at least 13,000 bushels of corn per year must be sold. (a) How much should farmers charge per bushel of corn to maximize annual revenue? HINT [See Example 3, and don't neglect endpoints.] (Round to the nearest cent.) p = $ (b) How much corn can farmers sell per year at that price? q = bushels per year (c) What will be the farmers' resulting revenue? (Round to the nearest cent) per year

Explanation / Answer

p = 6,600,000/q1.3

a)revenue =pq

=(6,600,000/q1.3)q

=(6,600,000/q0.3)

maximum revenue occurs when q is minimum. minimum value of q=13000

p = 6,600,000/130001.3

p=29.61

farmers should charge 29.61$per bushel of corn to maximize annual revenue

b)q=13,000 bushels of corn per year

c)farmers revenue =p*q=29.61*13,000=384911.54 dollars

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