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)=0.7x^2-420x+81,610. How many cars must be made to minimize the unit cost? Do not round your answer.

Answer 1

300 cars must be made to minimize the unit cost

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

It's vertex is the point

In which

Where

If a>0, the vertex is a minimum point, that is, the minimum value happens at
, and it's value is
.

The cost of producing x cars is given by:

So a quadratic equation with

How many cars must be made to minimize the unit cost?

This is the xvalue of the vertex. So

300 cars must be made to minimize the unit cost