Maximize Word Problem

[homeboy69]

In the 1930s a prominent economist devised the following demand function for corn:p =

6,590,000

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 7,000 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

 

[Steven G]

In the 1930s a prominent economist devised the following demand function for corn:p =

6,590,000

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 7,000 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

Can you please tell us where you got stuck?

 

[homeboy69]

Can you please tell us where you got stuck?

All 3 questions.

.(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

 

[stapel]

Can you please tell us where you got stuck?

All 3 questions.

Hmm... So you've been given a function:

. . . . .\(\displaystyle p\, =\, \dfrac{6,590,000}{q^{1.3}}\)

...where "p" stands for "the price in dollars for one bushel" and "q" stands for "the number of bushels that will be sold over the course of one year". You have been asked to find the maximum revenue (that is, the maximum income). You (should) know (from back in algebra) that the revenue will be the product of the per-item price "p" and the total number of items "q". You (should) know (from calculus) that derivatives are very helpful for finding max/min points. You are also given a "hint" regarding a specific (and thus directly helpful) worked example.

Since you still have absolutely no idea where to begin, clearly you need much more help than we can here provide. Did you take algebra before you were enrolled in calculus? If not, or if it's been many years, then you might want to speak with your academic advisor about a better course placement, so you can learn the algebra stuff that's necessary for doing the calculus.

Or perhaps you were exaggerating a bit, and you can reply showing some thoughts, efforts, and progress so far...?