I know this is a very simple problem, compared to most of what is posted here. I have a math assignment about functions, which I am terrible at. One of the questions in particular buggers me:
''A football club charges a fee of 75€ for a ticket every football match. Every football match the club expenses 75,000€ (fixed cost), and it is estimated to expense 15€ for each spectator. Let x be the number of spectators to the match.''
For clarification, the revenue of each football match will be 75€ per ticket purchased. The costs will be 15€ per attendee + a fixed cost (a cost which doesn't change per attendee) of 75000€.
On to the problem that I can't figure out:
Determine for the profit h(x) as a linear function of the number of spectators
This seems really simple to me, however, I cannot figure out the function I'm supposed to write... I'd some help with this.
There's another problem which frustrates me. It is a follow-up to this question: 'how many tickets should the club sell, to avoid a financial problem'. A financial problem is when costs exceed revenue. To calculate that, I used the following equation: $75x = 15x + 75,000$, with the result that the club should sell 1250 tickets to avoid a financial problem.
What I can't figure out, is the next question: Unfortunately, the number of spectators decreases, and it is hard to maintain the club without increasing the membership fee. The club manager says there are, on average, 1000 spectators each time. How much should be the new membership fee to avoid a financial problem?
I am utterly clueless as to what to do to answer this, and so would like some help.
I am sorry if this is not how I am supposed to formulate or set up any questions. It is my first post on here. I am sorry if I wrote way too much, but I was unsure as to how I should shorten it.
Thanks in advance!
We can represent profit, P, with the basic profit formula: $P =$ Total Revenue - Cost of Goods Sold.
Let's start with the Total Revenue as function of $x$, the number of spectators for a match. Since,
Our only source of revenue are the tickets sold, leaving us with a revenue equation: Total Revenue for a given match = $75x$
Now the costs are mentioned here:
Meaning the total cost is the fixed cost plus the variable cost, that varies according to $x$, which is the number of spectators at given match. This results in the following $$Total Cost = 75000 + 15x$$
Returning to the original profit formula, we can replace Total Revenue and Cost of Goods Sold (fancy way of saying Total Cost) with our equations, resulting in the following: $$P(x) = 75x - (75000+15x)$$ or $$P(x) = 60x - 75000$$
To find your break-even point, set profit = $0$ and solve for $x$. This will tell you the minimum number of spectators that must attend in order to break even.
You should have enough now to answer the rest of the questions.