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October 10th, 2017, 07:33 PM   #1
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Derivatives: Chain Rule - Marginal Revenue Product

I am having trouble with part c of this question. I have already solved A and B but if someone could help me with part c I would greatly appreciate it.

A factory owner who employs m workers finds they produce
q=1.2m(1.2m+46)^3/2
units of product per day

The total revenue R in dollars is
R= 586q / (245520+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 15 workers, the price per unit is 1.0852 dollars.

b) When there are 15 workers, the marginal revenue is 1.00 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= 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.

Last edited by canucks543; October 10th, 2017 at 07:36 PM.
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October 10th, 2017, 07:55 PM   #2
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$\dfrac{dR}{dm} = \dfrac{dR}{dq} \dfrac{dq}{dm}$

each of those derivatives is messy but straightforward.

yell back if you need help with them.
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