SOLUTION: The B & J co. wants to produce items at a minimum cost to the company. The cost of the items is modeled by the function C(x) = x^2 - 140 x + 5700, where x is the number of items pr

Question 1031235: The B & J co. wants to produce items at a minimum cost to the company. The cost of the items is modeled by the function C(x) = x^2 - 140 x + 5700, where x is the number of items produced.
A.) How many items should the company produce to keep the cost to a minimum?
B.) What is the minimum cost?
C.) When would the company have a cost of $0?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

(a)
When the equation has the form:
, then the
x-value of the vertex ( max or min ) is:

-----------------------
In this case:

70 items should be produced to make
cost a minimum
-------------------------
(b)
Plug into equation to get

The minimum cost is $800
------------------------
When does ?

complete the square

I can't take the square root of
both sides and get a real answer,
so the cost can never be zero
----------------------------
Here's the plot of :

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