A manufacturer of lighting fixtures has daily production costs of

Stefan Hendricks 2021-12-20 Answered
A manufacturer of lighting fixtures has daily production costs of C=80010x+0.25x2. where C is the total cost (in dollars) and X is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?
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Expert Answer

einfachmoipf
Answered 2021-12-21 Author has 32 answers
Step 1
Write the function in quadratic equation, f(x)=ax2+bx+c
C=0.25x210x+800
Step 2
The function has a minimum when x=b2a since a>0. Setermine the number of fixtures to be produced each day to yield a minimum cost. Let a=0.25 and b=10
x=b2a
x=102(0.25)
x=100.5
x=20
The manufacturer should produced 20 lighting fixtures daily to yield a minimum cost.

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Linda Birchfield
Answered 2021-12-22 Author has 39 answers
Step 1
To yield a minimum cost, the number of fixtures that should be produced daily is x=b2a. We know that a=0.25 and b=10
Step 2
Let us find the value of that x:
x=b2a
=(10)2×0.25 We substituted 0.25 for a and -10 for b
=100.5 We multiplied.
=20 We divided.
The number of daily produced fixtures should be 20.

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nick1337
Answered 2021-12-27 Author has 575 answers

Step 1
The total cost is given by:
y=0.25x210x+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=b2×a where the a and b come from:
ax2+bx+c=
the general form for the quadratic equation.
In your problem, a=0.25 and b=10
x=(10)2×(0.25) Simplify.
x=100.5
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.

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