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June 12th, 2017, 12:04 AM  #1 
Newbie Joined: Jun 2017 From: vancouver Posts: 3 Thanks: 0  Derivatives: Chain Rule  Marginal Revenue Product
All answers involve a unit of dollars, so you must enter your answers accurate to two decimal places! A factory owner who employs m workers finds that they produce q = 1.8m(1.8m+18)^3/2 units of product per day. The total revenue R in dollars is R=1544q / (344448+4q)^1/2 (a) From the fact that revenue = (price per unit)*(number of units) it follows that R=(price per unit)*q So when there are 10 workers, the price per unit is 2.5733 dollars. (b) When there are 10 workers, the marginal revenue is 2.52 dollars/(one unit of product). (c) The marginalrevenue product is defined as the rate of change of revenue with respect to the number of employees. Therefore, marginalrevenue product=dR/dm If q and R are given as above then, when m = 10, the marginalrevenue product is ? dollars/(one worker). This means that if employee number 11 is hired, revenue will increase by approximately ? dollars per day. Can't seem to find the answer for c. Last edited by skipjack; June 12th, 2017 at 10:55 AM. 
June 12th, 2017, 10:48 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 552 
Are you sure that a calculus answer is even wanted? I would probably attack this with difference equations rather than derivatives. 
June 15th, 2017, 08:15 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
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chain, derivatives, marginal, product, revenue, rule 
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