SOLUTION: Suppose that the cost function for a particular item is given by the equation C(x) = 2x2 − 360x + 16,420, where x represents the number of items. How many items should be

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Question 1011848: Suppose that the cost function for a particular item is given by the equation
C(x) = 2x2 − 360x + 16,420,
where x represents the number of items. How many items should be produced to minimize the cost?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can determine the minimum by either putting it into vertex form (algebraic method) or by taking the derivative (calculus method).
Vertex:
Convert to vertex form by completing the square.
C%28x%29=2%28x%5E2-180x%29%2B16420
C%28x%29=2%28x%5E2-180x%2B8100%29%2B16420-2%288100%29
C%28x%29=2%28x-90%29%5E2%2B16420-16200
C%28x%29=2%28x-90%29%5E2%2B220
So now the function is in vertex form.
The minimum of C%28x%29=220 occurs when x=90.
.
.
.
Derivative:
Find the derivative and set it equal to zero.
dC%2Fdx=4x-360=0
4x=360
x=90
Then,
C%2890%29=2%2890%29%5E2-360%2890%29%2B16420
C%2890%29=16200-32400%2B16420
C%2890%29=220