Question

The average cost per item, C, in dollars, of manufacturing a quantity q of cell phones is given by
C= (a/q) + b
where a and b are positive constants
a.Find the rate of change of C as q increases. What are its units?
b. Currently, 5000 phones are being made and production is increasing at a rate of 100 cell phones per week. How fast is the average cost changing if a = 200000? Is the average cost increasing or decreasing

for a i got C(q)= (a/q) + b
C'(q)= -(a/q^2) DOLLARS PER CELL PHONE.

for b) i started off as
dC/dt =-a/q^2 dq/dt =
(-200000/q^2).100
IM LOST AND NOT SURE WHAT TO DO PLEASE HELP ME

Answer 1

also can you please tell me if A is right? thank u

Answer 2

a, No.

YOu want dC/dq (which is cost/unit)

dC/dq=-a/q^2

b) dC/dt=-a/q^2 dq/dt
dC/dt=-2E5/25E6 *1E2=-20 dollars /week