SOLUTION: 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

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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