Related Rates Cell Phone Problem

[alyplayford]

Homework Statement

The average cost per item, C, in dollars, of manufacturing a quantity q of cell phones is given by the following equation, where a and b are positive constants.
C = a/q + b

(a) Find the rate of change of C as q increases. Include units.

I already found this, it's: -a/q^2

***(b) If production increases at a rate of 130 cell phones per week, how fast is the average cost changing? Include units.

B is the one I need help with.

The Attempt at a Solution

So far for part "b", I've figured out that dq/dt is 130, so I differentiated C = a/q + b implicitly
and got dC/dt = -a/q^2 (dq/dt) + b. I plugged in 130 for dq/dt and got

dC/dt = -130a/q^2 + b

I have no idea where to go from here.

Any help would be greatly appreciated!

 

[tiny-tim]

Hi alyplayford!

The average cost per item, C, in dollars, of manufacturing a quantity q of cell phones is given by the following equation, where a and b are positive constants.
C = a/q + b

(a) Find the rate of change of C as q increases. Include units.

I already found this, it's: -a/q^2

***(b) If production increases at a rate of 130 cell phones per week, how fast is the average cost changing? Include units.
…
So far for part "b", I've figured out that dq/dt is 130, so I differentiated C = a/q + b implicitly
and got dC/dt = -a/q^2 (dq/dt) + b. I plugged in 130 for dq/dt and got

dC/dt = -130a/q^2 + b

No, b is constant.

Now eliminate q from the RHS to get a differential equation in C.

 

[alyplayford]

What is RHS? And do I need to solve for q? How do I do that?

 

[tiny-tim]

What is RHS? And do I need to solve for q? How do I do that?

Right-hand side!

And C = a/q + b.