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)=0.5x^2-280x+48,205 . What is the minimum unit cost?

Do not round your answer.

Answer 1

=47,925.25

Explanation:

let x = 1

(0.5^2)-280+48,205

=47,925.25

Answer 2

The calculated minimum unit cost of the cars is $9005

How to determine the minimum unit cost of the cars

From the question, we have the following parameters that can be used in our computation:

C(x) = 0.5x² - 280x + 48,205

The x-coordinate of the vertex of the above function is calculated using

x = -b/2a

So, we have

x = 280/(2 * 0.5)

x = 280

The minimum unit cost of the cars is the y value at x = 280

So, we have

C(280) = 0.5 * 280² - 280 * 280 + 48,205

Evaluate

C(280) = 9005

Hence, the minimum unit cost of the cars is $9005