Thread: Finding minimum of average cost

A company has found that the total cost T(q) $ for product of q boxes can be calculated as:
T(q)=0.01q^2-2q+5000 , q>0
How many box has to be produced to the average cost of A(q)=T(q)/q become as low as possible?

Thanks for your help.

A(q) = T(q)/q = 0.01q - 2 + 5000/q

Now use what you know from calculus to minimize this (take derivative, set it to equal to 0, ...)
Also, q needs to be a natural number, so make sure to take this into account.

As a side note, what company pays $5000 for 0 boxes? [edit: never mind, q > 0]

A(q) = T(q)/q = 0.01q + 5000/q - 2


as A(q) is minimum, 0.01q=5000/q

q=500sqrt(2)

q=707(approx.)