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 unit

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?


Substitute 2000 for x

   P(x) = 2.25x - 7000 
P(2000) = 2.25(2000) - 7000 
P(2000) = 4500 - 7000
P(2000) = -$2500, a loss of $2500, since she hasn't
yet broken even when shoe has only sold 2000 units.

b what is her profit if she sells 5000 units?

   P(x) = 2.25x - 7000 
P(5000) = 2.25(5000) - 7000 
P(5000) = 11250 - 7000
P(5000) = $4250, she has broken even and made
$4250 besides.


c what is the break-even point for sales? 

That's when she has neither made nor lost any money,
which means when her profit is 0

So we set the profit = 0

   P(x) = 2.25x - 7000 
      0 = 2.25x - 7000

Add 7000 to both sides
    
    7000 = 2.25x
3111 1/9 = x

Since that is a fraction, we must round it
the next higher integer, 3112, for when she
sells 3111 she has a very small loss, and
when she sells 3112, she has a very small 
gain.  So she begins to make money when
she sells the 3112nd unit.

Edwin