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February 8th, 2011, 10:51 PM   #1
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Calculus:Chain Rule - Marginal Revenue Product

A factory owner who employes m workers finds that they produce

q= 1.8m(1.8m+9)^3/2 units of product per day.

The total revenue R in dollars is

R=1029q / (336672+4q)^1/2


(c) The marginal-revenue product is defined as the rate of change of revenue with respect to the number of employees. Therefore,
marginal-revenue product=dR/dm

If q and R are given as above then, when m= 15, the marginal-revenue product is _________ ? dollars/(one worker). This means that if employee number 16 is hired, revenue will increase by approximately _________? dollars per day.
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February 8th, 2011, 11:35 PM   #2
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Re: Calculus:Chain Rule - Marginal Revenue Product

As this is a calculus problem, I've moved the topic to the Calculus sub-forum. Also, I deleted the duplicate topic, as a question only needs to be posted once. One of the duties of moderating is keeping the forum clear of redundancy. I hope you find this reasonable, as I am not trying to keep you from getting a solution.

That being said, welcome to the forum! You are encouraged to post questions, just pick the most appropriate sub-forum and post the question once.

To find we will need:

(1)

(2)

(3)

Starting with (3) we have:



Continuing with (2) we find:



When m = 15, then we have:



Finally with (1) we find:





When q = 5832, we have:



Now, using the chain rule, we have:

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February 17th, 2013, 11:18 PM   #3
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Re: Calculus:Chain Rule - Marginal Revenue Product

Im a little confused what is the answer to the first blank?
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