Related Rates Question: How to Solve and Understand Using Equations

[Slimsta]

Homework Statement

http://img25.imageshack.us/img25/1937/38821874.jpg

Homework Equations

in the picture

The Attempt at a Solution

im really confused!
im not sure if i did it right in the picture but i pretty much guessed them all.. (with thinking obviously)
the first one is easy because its just multiplying the whole equation by q..
dq/dt is the product/day right? so 180..
for some reason, i think that q=40 and i cannot explain why not 180
can someone please explain the problem to me? pleasezzz!

 

[HallsofIvy]

Yes, since selling q things for p dollars per thing, you make pq dollars, the total daily revenue is pq= q(40- q/180)= 40q- q²/180.

The marginal rate of revenue (as opposed to the average rate of revenue) is dR/dt= dR/dq dq/dt= (40- q/90)(dq/dt) and you are told that "daily production is 180" and that "A company is increasing production at 40 units per day" so q= 180 and dq/dt= 40. dR/dt= (40- 180/90)(40).= (40-2)(40)= 1520 dollars per day on that particular day.

dq/dt is the product/day right?

No. q is the product/day. dq/dt is the rate of change of production per day and you are told that it is 40.

 

[Slimsta]

oh thanks man!
i kinda was doing the same thing just had the numbers mixed up.
and i didnt know that dR/dq = (40- q/90).. i thought its dR/dt...