Question 1117653
<font face="Times New Roman" size="+2">


The cost function, *[tex \Large C(x)], where *[tex \Large x] is the number of items <b>manufactured</b> is the sum of the fixed costs plus the variable costs.  Since it costs $0.10 for every item manufactured, the total variable cost is *[tex \Large 0.10x] while the fixed cost is given as $1000.  Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C(x)\ =\ 0.10x\ +\ 1000]


The Revenue function, *[tex \Large R(x)] where *[tex \Large x] is the number of items <b>sold</b>, is simply the sell price per item, here *[tex \Large $0.60] times the number sold.  Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R(x)\ =\ 0.60x]


In this simplistic scenario, we are given that the number sold is equal to the number manufactured, so the value of the independent variable in each function is the same.


The break-even point is the number of items manufactured and sold such that the value of the revenue function is equal to the cost function:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R(x)\ =\ C(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0.60x\ =\ 0.10x\ +\ 1000]


Solve for *[tex \Large x]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>