SOLUTION: 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 (c) What i

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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 (c) What i      Log On


   

Question 74203: 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
(c) What is the break-even point for sales?
This is exercise 53 below:
Business and Finance. If the inventor of a new product believes that the cost of producing the product is given by the function
C(x)= 1.75 + 7000
How much does it cost to produce 2000 units of her invention?
$10,500
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The break-even point is when the profit is 0. So if we set p(x)=0 we could find x
0=2.25x-7000
7000=2.25x
7000%2F2.25=x
x=28000%2F9=3111.1111
So if she sells about 3,111 units then she breaks even.


Check:
p%28x%29=2.25x-7000Plug in x=3111.11
0=2.25%2828000%2F9%29-7000
0=7000-7000
0=0Works


I'm assuming the function looks like
C%28x%29=1.75x%2B7000So just plug in 2000 for x
C%282000%29=1.75%282000%29%2B7000
C%282000%29=3500%2B7000
C%282000%29=10500
So it costs $10,500 to produce 2000 units.