The minimum of the function is at the vertex of the parabola represented by the equation.
The x-coordinates is the number of jeans that should be produced in order to minimize costs.
The y-coordinate is the minimum cost.
[tex]C(x)=0.2x^2-96x+12095 \\
a=0.2 \\ b=-96[/tex]
The vertex of a parabola is (h,k), where:
[tex]h=\frac{-b}{2a}=\frac{-(-96)}{2 \times 0.2}=\frac{96}{0.4}=240 \\ \\
k=C(h)=C(240)=0.2 \times 240^2-96 \times 240+12095= \\
=11520-23040+12095=575[/tex]
240 jeans should be produced each day in order to minimize costs. The minimum daily cost is $575.
