Question 71252
The total cost is given by:
{{{y = 0.25x^2-10x+800}}}
Find the value of x that will give the minimum y.
Notice that the equation is that of a parabola that opens upward.  So if you can find the vertex of this parabola, you will have found the minimum.
The x-coordinate of the vertex of a parabola can be found by:
{{{x = (-b)/2a}}} where the a and b come from:{{{ax^2+bx+c=0}}} the general form for the quadratic equation.
In your problem, a = 0.25 and b = -10
{{{x = (-(-10))/2(0.25)}}} Simplify.
{{{x = 10/0.5}}}
{{{x = 20}}}
So 20 fixtures should be produced each day to yield a minimum cost.
If you wanted to find this minimum cost, you would simply substitute x=20 into the original equation and solve for y.