Question 1194244
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Part A


x = number of records made and sold


The initial investment is $5,000.
It costs $4 to make each disc, and there's an extra $1 in cost for copyright purposes. So it really costs 4+1 = 5 dollars per disc.
If the company creates x records, then they spend 5x dollars on top of the $5000 invested.
The cost function is C(x) = 5x+5000


The revenue function is R(x) = 15x because the selling price is $15 per record. 
This is the amount of money pulled in before costs are considered. 


Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 15x - (5x+5000)
P(x) = 15x - 5x-5000
P(x) = 10x - 5000


Answer: <font color=red>P(x) = 10x - 5000</font>


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Part B


I'm assuming you're looking for the break-even point.


This occurs when the profit is 0 dollars (see method 1 below)
In other words, it happens when revenue and cost are the same amount (see method 2).


Method 1
Profit = 0
P(x) = 0
10x - 5000 = 0
10x = 5000
x = 5000/10
x = 500


Method 2
Revenue = Cost
R(x) = C(x)
15x = 5x+5000
15x-5x = 5000
10x = 5000
x = 5000/10
x = 500


If 500 records are made and sold, then the company will break even. 
They will neither lose money nor gain money.


Answer: <font color=red>500 records</font>



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Part C


Replace P with 100,000 and solve for x.
P(x) = 10x - 5000
100,000 = 10x - 5000
10x-5000 = 100,000
10x = 100,000 + 5000
10x = 105,000
x = 105,000/10
x = 10,500


Answer: <font color=red>10,500 records</font>


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Part D


Plug in x = 200 into the profit function
P(x) = 10x - 5000
P(200) = 10(200) - 5000
P(200) = 2000 - 5000
P(200) = -3000
A negative profit means the company lost money.


Notice that x = 200 is smaller than the break-even point we found back in part B.
The company must make more than 500 records to have a positive profit.


Answer: <font color=red>-3000 dollars</font>
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