We are given the equation:
C = (16,000 / r) + (26πr^2 / 3)
<span>First get the 1st derivative:</span>
dC/dr = (-16,000 / r^2) + (52π r / 3)
Equate dC/dr to get the minima:
(-16,000 / r^2) + (52π r / 3) = 0
Multiply everything by r^2:
-16,000 + (52π/3) r^3 = 0
r = 6.65
Therefore the cost at radius = 6.65 is:
C = (16,000 / 6.65) + (26π (6.65)^2 / 3)
C = 3,610.07
So perhaps the interval interest is (0, 3,610.07] if cost or (0, 6.65] if based on radius.
