SOLUTION: A manufacturer of lighting fixtures has daily production costs modeled by y=0.25x^2-10x+800 where y is the total cost in dollars and x is the number of fixtures produced How man

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Question 71252: A manufacturer of lighting fixtures has daily production costs modeled by y=0.25x^2-10x+800 where y is the total cost in dollars and x is the number of fixtures produced
How many fixtures should be produced each day to yield a minimum cost?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The total cost is given by:
y+=+0.25x%5E2-10x%2B800
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+=+%28-b%29%2F2a where the a and b come from:ax%5E2%2Bbx%2Bc=0 the general form for the quadratic equation.
In your problem, a = 0.25 and b = -10
x+=+%28-%28-10%29%29%2F2%280.25%29 Simplify.
x+=+10%2F0.5
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.