Minimizing Cost?

Question

A company uses the formula C(x)=0.02x^2-3.4x+150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?

Answer 1

The minimum cost is 5.5 when x = 85 bars.

You can use calculus to get the minimum (.02*2x - 3.4 = 0, so x = 3.4 / .04 = 85), or you could plug the formula into a spreadsheet and notice that the cost decreases until it gets to 85 and then starts increasing.