Ticket prices - quadratic/linear system

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pianobyear

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Greetings,

I'm glad this forum is here, so I can present this as an example of a problem I found that doesn't seem to make sense:

The revenue for the school play is given by: R = -50t + 300t, where “t” is the ticket price in dollars. The cost to produce the play is given by: C = 600 - 50t. Determine
the ticket price that will allow the company to break even.

It seems odd that the ticket price is affecting both cost and revenue. I also can't see any practical reason why there's an x2 in the cost equation. Is this just a hypothetical problem posed by a teacher, or could such a scenario really exist? The only cost per attendee seems to be program printing, but you'd want to have more printed than you're likely to use and if attendance is low, it probably wouldn't get you out of a run to the printer.

Thanks, all
 
pianobyear said:
Greetings,

I'm glad this forum is here, so I can present this as an example of a problem I found that doesn't seem to make sense:

The revenue for the school play is given by: R = -50t + 300t, where “t” is the ticket price in dollars. The cost to produce the play is given by: C = 600 - 50t. Determine
the ticket price that will allow the company to break even.

It seems odd that the ticket price is affecting both cost and revenue. I also can't see any practical reason why there's an x2 in the cost equation. Is this just a hypothetical problem posed by a teacher, or could such a scenario really exist? The only cost per attendee seems to be program printing, but you'd want to have more printed than you're likely to use and if attendance is low, it probably wouldn't get you out of a run to the printer.

Thanks, all
Click to expand...

As a more general answer to your question, your profit depends on how many tickets are sold, and the price at which they are sold. Too low a price means you don't make enough money to cover your costs (which may also depend on the number of tickets sold - for example, more tickets means more chairs need to be hired), but too high a price means that people won't buy the tickets. If you modelled this phenomenon, you would get a Quadratic equation with a maximum value for the profit - hence the square term.

(The more specific reason for a quadratic is because the profit is proportional to both ticket price and the number of tickets sold, therefore a product of two linear functions, i.e. a quadratic function.)
 
Denis said:
Hmmm...if R = C, then:
-50t + 300t = 600 - 50t : t = 2 ($2 per ticket...I'll buy 5!).
But that seems too ridiculously easy...
Click to expand...
Denis, I sell tickets for $1.5. Can I put you down for 10?
 
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