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)=0.5x²-130x+21,756. What is the minimum unit cost?
Do not round your answer.
Unit cost: $
X
5

Answer 1

To find the minimum unit cost, we need to find the vertex of the parabola represented by the function C(x). The x-coordinate of the vertex can be found by using the formula x=-b/2a, where a=0.5 and b=-130 in this case. Plugging in those values, we get x=130/1=130.

To find the corresponding minimum unit cost, we need to evaluate the function at x=130. Plugging in x=130, we get C(130)=0.5(130)^2-130(130)+21,756=8,556. Therefore, the minimum unit cost is $8,556.

The table with x=5 is irrelevant to finding the minimum unit cost.