Question 122219: Solve the following applications involving functions.
10. Business and finance. If the inventor in exercise 53 charges $4 per unit, then her profit for producing and selling x units is given by the function
P(x) = 2.25x – 7000
(a) What is her profit if she sells 2000 units?
(b) What is her profit if she sells 5000 units?
(c) What is the break-even point for sales?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! a)
 Start with the given function.
 Plug in 
 Multiply 2.25 and 2,000 to get 4,500
 Subtract 7,000 from 4,500 to get -2,500
So her profit is -2,500 dollars when she sells 2,000 units. In other words, she loses 2,500 dollars when she sells 2,000 units.
b)
Start with the given function.
 Plug in 
 Multiply 2.25 and 5,000 to get 11,250
 Subtract 7,000 from 11,250 to get 4,250
So her profit is 4250 dollars when she sells 5,000 units
c)
What is the break-even point for sales? The break even point occurs when 
Start with the given function.
 Replace  with 0
 Subtract 2.25x from both sides
 Divide both sides by -2.25
 Divide
So if you round to the nearest whole number, you get
So the break-even point is when she sells about 3,111 units
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