Question 972138
<font face="Times New Roman" size="+2">


To achieve zero inventory, the demand must be greater than or equal to the supply.  Since the demand is *[tex \Large D\ =\ -2000p^2\ +\ 2000p\ +\ 17000] and the supply is 5000, solve the following inequality for *[tex \LARGE p]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2000p^2\ +\ 2000p\ +\ 17000\ \geq\ 5000]


Note that no matter how great the demand is, the inventory cannot be less than zero -- once the bottles are gone, they are gone, no matter how many people want more.  Therefore we are solving an inequaltiy.  If the question had asked, "What is the <i>greatest price</i> that will result in zero inventory?" then you would be solving the <i>equation</i>:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2000p^2\ +\ 2000p\ +\ 17000\ =\ 5000]


Good luck.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \