Question 70361
From the way this problem is worded, the equation for C(x) is not needed to answer the questions
that are asked.  The only equation that applies is:
.
{{{P(x) = 2.25x - 7000}}}

The first question ... What is the profit if she sells 2000 units?  Calculate the profit by
setting x equal to 2000 units so that the equation becomes:
.
{{{P(x) = (2.25)*(2000) - 7000 = 4500 - 7000 = -2500}}}
.
The negative sign tells you that overall she loses $2500 if she sells only 2000 units.
.
The second question ... What is the profit if she sells 5000 units?  Do the same calculation
as above, but this time set x equal to 5000 units so that the equation becomes:
.
{{{P(x) = (2.25)*(5000) - 7000 = 11250 - 7000 = 4250}}}
.
The positive answer tells you that overall she makes $4,250 if she sells 5000 units.
.
So somewhere between sales of 2000 units (a loss) and selling 5000 units (a gain) she
reach a break-even point.  At that break-even point her profit would be zero (neither a
loss nor a gain).  So this time set the profit equal to zero in the equation and solve the
resulting equation for x.
.
{{{0 = (2.25)*x - 7000}}}
.
Add 7000 to both sides and transpose the equation:
.
{{{2.25*x = 7000}}}
.
Divide both sides by 2.25 to get:
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{{{x = 7000/2.25 = 3111.11}}}}
.
This result tells you that if she sells less than this amount she loses money, but if
she sells more than this number of units she makes money.  Therefore, you can say that
she loses a very small amount of money if she sells 3111 units, and she makes a very small
amount of money if she sells 3112 units.
.
Hope this helps you to see your way through the problem ... especially with regarding
the information on the costs involved with production, C(x), and the sales price of $4.00
per unit. That information was not needed because you were provided with an
equation that 
directly calculates profit based on the number of units sold.