Derivatives: Chain Rule - Marginal Revenue Product?

Question

All answers involve a unit of dollars, so you must enter your answers accurate to two decimal places!
A factory owner who employes m workers finds that they produce

q= 2.2m(2.2m+3)^3/2 units of product per day.

The total revenue R in dollars is

R=716q / (231588+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 15 workers, the price per unit is ? dollars.

(b) When there are 15 workers, the marginal revenue is ? 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.

Answer 1

"Derivatives: Chain Rule - Marginal Revenue Product?"

Calculus: Vectors -Trigonometry Triangle Equation.

Answer 2

A.) you just plug in 15 for m in the first equation (q= 2.2m(2.2m+3)^3/2) to get 7128.

Then you take 7128 and put it in for q in the second equation and you end up with some number like 10 007.15294...



The revenue function will then look like 10 007.15294...=(price per unit) * 7128.



Then you want price per unit by itself so you divide both sides by 7128 and you get your answer which is 1.40.



B.) You take the derivative of R=716q / (231588+4q)^1/2 which would = 179(q + 115794) / (q+57 897)^(3/2)



NOTE: a helpful link http://library.wolfram.com/webMathematica/Education/WalkD.jsp It's a derivative calculator ;)



Then you just plug 7128 into the derivative to get the answer for B.



And sorry I didn't get the last one either.



BTW you go to SFU don't you. This is one of the loncapa questions right? You're in Menz's clas probably right :)

Answer 3

f(x) = [4x² + 9]^4 × [-9x² + 5]^13 Use the Product rule for derivatives which requires use of the Chain rule. f’(x) = 4[4x² + 9]^3[8x][-9x² + 5]^13 + [4x² + 9]^4(13)[-9x² + 5]^12[-18x] I will let you simplify this expression, notice all the common factors. ProfRay Sorry, no shortcuts. It is just grunt work. Most derivatives are that way!!