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20 votes
20 votes
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.

User Agrawal Shraddha
by
2.4k points

1 Answer

17 votes
17 votes

Answer:

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:


image

It's vertex is the point
image

In which


image


image

Where


image

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

The cost of producing x cars is given by:


image

So a quadratic equation with
image

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

This is the xvalue of the vertex. So


image

300 cars must be made to minimize the unit cost

User Dezhik
by
2.7k points