A manufacturer of lightweight, durable containers is contracted to make cylindrical containers to hold liquid. They find that the manufacturing cost depends on the radius of the cylinder they make

Question

A manufacturer of lightweight, durable containers is contracted to make cylindrical containers to hold liquid. They find that the manufacturing cost depends on the radius of the cylinder they make, according to the equation

C(r) = 7(pi)(r²)+(377/r)

What radius will minimize the cost?

Answer 1

C'(r) = 14πr - 377/r² = 0; 14πr³ = 377; r = (377/(14π))^1/3 = 2.047 units of length

C''(r) = 14π + 754/r³ > 0 for all r. So, we have minimum