Question 1196506
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Part (a)


x = number of magazines made and sold
0.40x = cost of printing x magazines, at $0.40 per magazine, before the $1400 fixed cost
0.40x+1400 = add on the $1400 fixed cost


Answer: C(x) = 0.40x+1400


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Part (b)


revenue = amount of money coming in
revenue = (number of magazines sold)*(price per magazine)
revenue = (x)*(1.05)
revenue = 1.05x


Answer: R(x) = 1.05x


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Part (c)


Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 1.05x - (0.40x+1400)
P(x) = 1.05x - 0.40x - 1400
P(x) = 0.65x - 1400


Let's find the break-even point. 
This is when the profit is $0
It is when the company neither loses money nor gains it.


Replace P(x) with 0. Solve for x.
P(x) = 0.65x - 1400
0 = 0.65x - 1400
1400 = 0.65x
x = 1400/0.65
x = 2153.84615384616 approximately
x = 2154


Let's see what the profit is for x = 2153 and x = 2154
P(2153) = 0.65*2153 - 1400 = -0.55
P(2154) = 0.65*2154 - 1400 = 0.1


Selling x = 2153 units produces a negative profit
Selling x = 2154 units is when the profit finally becomes positive. 
Any larger x value will have P(x) > 0 since P(x) is linear.


Answer: The company must sell 2154, or more, magazines to make a profit.
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