To find the minimum cost of manufacturing wheels, we need to determine the vertex of the quadratic function C(x).
The function C(x) is in the form of a quadratic equation: C(x) = ax^2 + bx + c, where a = 0.1, b = -60, and c = 22744.
The x-value of the vertex is given by the formula x = -b / (2a). Let's calculate that:
x = -(-60) / (2 * 0.1)
x = 60 / 0.2
x = 300
The x-value of the vertex is 300. To find the corresponding y-value, we substitute x = 300 into the equation C(x):
C(300) = 0.1(300)^2 - 60(300) + 22744
= 9000 - 18000 + 22744
= -9000 + 22744
= 13744
Therefore, the minimum cost of manufacturing wheels is $13,744.