My Math Forum Derivatives: Chain Rule - Marginal Revenue Product

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 October 10th, 2017, 07:33 PM #1 Newbie   Joined: Oct 2017 From: Surrey Posts: 5 Thanks: 0 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.
 October 10th, 2017, 07:55 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,530 Thanks: 1390 $\dfrac{dR}{dm} = \dfrac{dR}{dq} \dfrac{dq}{dm}$ each of those derivatives is messy but straightforward. yell back if you need help with them.

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