Question 1139591
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I think you meant to say {{{C=(1/30)x^2-2x+2530}}} instead of {{{C=1/30 x^2-2x+2530}}}
The difference is that the {{{x^2}}} term is not in the denominator. 
To make sure you do not divide by {{{x^2}}}, 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
{{{y = ax^2 + bx + c}}}
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.
{{{f(x) = (1/30)x^2-2x+2530}}}


{{{f(30) = (1/30)(30)^2-2(30)+2530}}} Replace every x with 30; use PEMDAS to simplify


{{{f(30) = (1/30)(900)-2(30)+2530}}}


{{{f(30) = 30-60+2530}}}


{{{f(30) = 2500}}}


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 {{{a > 0}}} (in this case, a = 1/30 = 0.033 approximately)


The graph confirms the answer
<img src = "https://i.imgur.com/DMiBMjm.png">
The graph was created with <a href = "https://www.geogebra.org/">GeoGebra</a> (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 <font color=red size=4>2500 dollars</font>
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