Question 1160487
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The profit as a function of the number of units sold, *[tex \Large x], is *[tex \Large P(x)] and is equal to the difference between revenue as a function of *[tex \Large x], *[tex \Large R(x)], and cost as a function of *[tex \Large x]:


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


In this problem, your revenue function is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R(x)\ =\ 10.5x]


The cost function is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ C(x)\ =\ 6x\ +\ 8000]


"Break even" means you make zero profit, i.e., no gain, and no loss. So in order to solve the second question, you have to solve:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10.5x\ -\ (6x\ +\ 8000)\ =\ 0]


If this has an integer solution, then you have an exact answer for the break-even point.  But if you don't have an integer solution, you need to round your answer to the next higher whole number.  That is because rounding down will result in a small loss whereas rounding up gives you a small gain, and you have to meet or exceed break-even in this case.


In the case of obtaining an integer solution, you need to add one to the answer to get the answer to question 1.  If no integer solution, then the answer to the first two questions is the same.


For the third question solve:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10.5x\ -\ (6x\ +\ 8000)\ =\ 800000]
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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