SOLUTION: if the inventor 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 un

Algebra ->  Graphs -> SOLUTION: if the inventor 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 un      Log On


   

Question 123093: if the inventor 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?
Please show work......
I am completely confused
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe the way the equation is given is confusing you... x is a variable in the equation which represents the number of units sold. P(x) is an expression of the Profit in terms of number of units sold. So, to figure out the profit, just plug in the given value for number of unit sold, which is x, and solve the equation:
a.) what is her profit if she sells 2000 units?
P%28x%29=2.25x-7000
Plug in 2000 for x:
P%282000%29=2.25%282000%29-7000
highlight%28P%2820000%29=-2500%29
Note the answer is negative, so she lost money selling only 2000 of these.
b.)what is her profit if she sells 5000 units?
Plug in 5000 for x:
P%285000%29=2.25%285000%29-7000
I will let you do the math to finish this one...
c.) what is the break even point for sales?
The break even point is by definition when the profit is exactly zero. So equate the given expression to zero, and solve for x:
2.25x-7000=0
2.25x=7000
x=3111.1
Since you can't sell a tenth of a unit, just round it to the nearest whole unit:
highlight%28x=3111%29
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Good Luck,
tutor_paul@yahoo.com