Question 1139591: The cost C (in dollars) for a company to produce and sell x thousand gadgets is given by 
What is the minimum cost?
I've found that the start up cost is 2530 dollars.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
I think you meant to say  instead of
The difference is that the  term is not in the denominator.
To make sure you do not divide by , you would write it like this
C = (1/30)x^2 - 2x + 2530
If my assumption is correct, then we have an equation in the form
where
a = 1/30
b = -2
c = 2530
Use the 'a' and 'b' values to compute the value of h, which is the x coordinate of the vertex
h = -b/(2a)
h = -(-2)/(2*(1/30))
h = 2/(2/30)
h = (2/1) / (2/30)
h = (2/1) * (30/2)
h = (2*30)/(1*2)
h = 60/2
h = 30
The x coordinate of the vertex is 30.
The y coordinate of the vertex is k, which is defined as k = f(h)
For this problem, k = f(30)
In other words, we plug in x = 30 to find the y coordinate of the vertex.
 Replace every x with 30; use PEMDAS to simplify
We see that k = 2500, meaning the y coordinate of the vertex is 2500.
The vertex is at (h,k) = (30, 2500) which in this case is the lowest point of the parabola. The parabola has a lowest point any time  (in this case, a = 1/30 = 0.033 approximately)
The graph confirms the answer
The graph was created with GeoGebra (free graphing software). I used the "min" feature in GeoGebra to find/display point A as shown in the diagram above.
The vertex point (30, 2500) means that if you produce and sell 30 thousand gadgets, then the minimum cost is $2500
side note: keep in mind that x is in thousands. So x = 30 really means 30,000.
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Answer:
The minimum cost is 2500 dollars
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