The cost C, per car, is given by C(n)=0.3n^2-90n+12,450, where n represents the number of cars produced. Dtermine the lowest per car cost?

Question

The daily cost per car manufactured at a certain automotive plant decreases as the number of cars increase and then increases again due to overtime production costs. The cost C, per car, is given by C(n)=0.3n^2-90n+12,450, where n represents the number of cars produced. Dtermine the lowest per car cost?

Answer 1

Respectfully, I disagree with Sam Z.

The cost function is a quadratic with a minimum point at n=150, determined by setting the derivative = 0, i.e. .6n-90=0.

C(150)=5700.

Answer 2

Either 100 or 200 works. Each figure comes to 6450. It would be better to go with 200.

I put this formula into my calculator.