Answers:
To reach the breakeven point, how many attendees will that take? 117
What will be the company's total expenses and revenues? $1755 for each
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Explanation:
x = number of attendees
C(x) = cost function for the company
C(x) = 14x+117
This is because the company pays $14 per person, so x of them accounts for 14x dollars. Then we add on the flat fee of $117 to get 14x+117 dollars overall.
In contrast, the revenue is
R(x) = 15x
because each attendee brings in $15 for the company
The breakeven point is when the cost and revenue are the same. This produces a profit of $0.
R(x) = C(x)
15x = 14x+117
15x-14x = 117
x = 117
If 117 people attend the seminar, then the company breaks even.
To check this, we'll compute the cost and revenue
C(x) = 14x+117
C(117) = 14*117+117
C(117) = 1755
R(x) = 15x
R(117) = 15*117
R(117) = 1755
The cost and revenue is $1755 for each. Because we get the same value, this confirms the correct x value.
Since 117 people is the breakeven point, the company should aim for an attendee count above this, so they can get a positive profit. At some point, there is a max capacity so x can't go up forever.
