Question

CALCULUS HELP

A prominent economist devised the following demand function for corn:
p = 6,630,000/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 8,000 bushels of corn per year must be sold.

(a) How much should farmers charge per bushel of corn to maximize annual revenue?

(b) How much corn can farmers sell per year at that price?


(c) What will be the farmers' resulting revenue?

Answer 1

It's \[p=6,630,000 \div q^ \left( 1.3 \right)\]

Answer 2

Does anyone know?

Answer 3

I don't know where to start

Answer 4

\[p=\frac{6630000}{q^{1.3}}\]is the price per bushel. q is the number of bushels.

So qp will be the total price for all of the bushels.\[q\times p =\frac{6630000}{q^{0.3}}\]in the domain\[D=[8000,\infty) \cup \mathbb{Z}\]is the function for the total annual revenue.

We know that a function of the form\[y=\frac{1}{x^{0.3}}\]gets smaller as x increases, so in order to maximize profit q should be 8000.

That's how I'm thinking about the problem anyway. I can't think of another way to do it. I hope that helps.

Answer 5

Thanks that worked!

Answer 6

You're welcome!