Question

A vehicle factory manufactures cars. The unit cost c (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function c(x)=1.1x^2-660x+107,357. How many cars must be made to minimize the unit cost?

Do not round your answer.

Answer 1

300

Explanation:

The vertex of quadratic ax^2 +bx+c is on the line x=-b/(2a). This unit cost function defines a parabola opening upward, so its vertex is its minimum. The location of the vertex is ...

x = -(-660)/(2·1.1) = 660/2.2 = 300

300 cars must be made to minimize the unit cost.

_____

Note:

The unit cost at that production level will be $8357.