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February 2nd, 2014, 11:53 PM   #1
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Derivatives: Chain Rule - Marginal Revenue Product

I solved part a and b but I am confuse with part c. Is there any one who can help me??


A factory owner who employes m workers finds that they produce

q=1.4m(1.4m+50)^(3/2)
units of product per day.

The total revenue R in dollars is
R=754q/(255760+5q)^(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 1.3963 dollars.



(b) When there are 10 workers, the marginal revenue is 1.31 dollars/(one unit of product).



(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= 10, the marginal-revenue product is___________ dollars/(one worker). This means that if employee number 11 is hired, revenue will increase by approximatel______ dollars per day.
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February 3rd, 2014, 03:05 AM   #2
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Re: Derivatives: Chain Rule - Marginal Revenue Product

IN part c you can use the chain rule.

Or, you can put q in terms of m in the equation R=... and differentiate when R is a function of m instead of q.
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