1. The Marginal Revenue

For the equations below, q is the total number of units produced per day by m employees of a manufacturer, and p is the price per unit at which the q units are sold.
Find the marginal-revenue product for the given value of m.

q = (500m - m^2)/50, p = -0.3q + 90; m = 70

2. Re: The Marginal Revenue

Originally Posted by joshuaa
For the equations below, q is the total number of units produced per day by m employees of a manufacturer, and p is the price per unit at which the q units are sold.
Find the marginal-revenue product for the given value of m.
q = (500m - m^2)/50, p = -0.3q + 90; m = 70
Revenue $r(m)=q(m)\cdot p(m)$ price times quantity sold.
Marginal revenue ia $mr(m)=r'(m)$ the derivative of revenue.
$mr(m)=q'(m)p(m)+q(m)p'(m)$ You want $mr(70)$.

3. Re: The Marginal Revenue

r'(m) = (500 - 2m)/50 . [ -0.3((500m - m^2)/50) + 90 ] + [ -0.3(500 - 2m)/50 . (500m - m^2)/50

r'(70) = 7.2 . (-90.6) + (-2.16) . 602 = -1952.64

How is it negative?

4. Re: The Marginal Revenue

That is a rate of change. As you change the number of employees, you change the revenue. As the number of employees reaches 70, the revenue is decreasing at a rate of about 2000 per employee. To approximate the revenue with 71 employees, you could calculate the revenue with 70 employees and subtract 2000. Similarly, to approximate the revenue with 69 employees, you could calculate the revenue with 70 employees and add 2000. That will give you an estimate only. The further away from 70 employees you get, the less accurate the estimate becomes.

5. Re: The Marginal Revenue

Does this means I got a correct answer?

6. Re: The Marginal Revenue

Actually, it appears your equations are wrong. It appears that price winds up being negative. I would guess that $p = -0.3m+90$ not $p=-0.3q+90$.

7. Re: The Marginal Revenue

I am sure it is p = -0.3q + 90

8. Re: The Marginal Revenue

Originally Posted by joshuaa
I am sure it is p = -0.3q + 90
Then the question is nonsensical. At $m=70$, you are paying people to take the product from you. The problem would make sense at $m=700$. Did you miss a zero?

10. Re: The Marginal Revenue

Originally Posted by joshuaa
Having changed m to x (to avoid the program seeing meters) HERE is what we get:

r(x)= SEE HERE

11. Re: The Marginal Revenue

WolframAlpha website give me this equation r(x) = -0.00012x^4 + 0.12x^3 - 31.8x^2 + 900x

r'(70) = -1952.64 which is the same result i got above

what do you think? Is my answer Correct?

12. Re: The Marginal Revenue

Originally Posted by joshuaa
WolframAlpha website give me this equation r(x) = -0.00012x^4 + 0.12x^3 - 31.8x^2 + 900x
r'(70) = -1952.64 which is the same result i got above
what do you think? Is my answer Correct?
That is a correct answer to the question as written.

T too suspect that the question is faulty.

13. Re: The Marginal Revenue

Thanks a Lot.