Answer:
130 cars
Explanation:
You want the value of x (the number of cars made) that minimizes the unit cost, given by C(x) = 0.4x² -104x +13586.
Vertex
The minimum cost will be found at the vertex of this quadratic cost function. For quadratic ax²+bx+c, the vertex is found at x=-b/(2a).
The cost function has a=0.4 and b=-104, so the number of cars that must be made to minimize the unit cost is ...
x = -b/(2a) = -(-104)/(2(0.4)) = 104/0.8
x = 130
130 cars must be made to minimize the unit cost.
__
Additional comment
A graphing calculator can plot the cost function and show you the coordinates of the minimum cost. The attachment shows the minimum cost per car is $6826 when 130 cars are made.