Community Night: A Budget With One Bad Line Item
The Greendale Youth Council has $2,400 and five weeks to run a community night at the town center. Council rules require at least 8% of the total budget to remain unspent when the event closes. Committed costs are a $180 custodial fee, $340 for table and chair rental, and $120 for decorations and supplies. The venue's posted occupancy limit is 140 people. RSVPs currently stand at 96 and close three days before the event; the count was 74 four days ago. Last year, 90 RSVPs produced 104 attendees because of walk-ins. Two caterers have quoted. Vendor A charges $9.50 per person in multiples of ten, but the order locks seven days before the event with no changes afterward. Vendor B charges $6.80 per person with a 200-plate minimum and will adjust numbers up to 72 hours before. A local DJ has offered to play for $450. Amplified sound from an outside vendor requires a $75 permit; the center's own speaker system is free to use with a phone playlist and needs no permit. The treasurer wants to book the DJ.
1. Calculate what is genuinely available for food and extras, and identify the constraint that decides the plan.
Read the worked answer
The reserve is 8% of $2,400, or $192. Fixed commitments are $180 + $340 + $120 = $640. So the pool available for food and anything discretionary is $2,400 − $192 − $640 = $1,568.
Now test the DJ against that pool. The DJ plus the amplified-sound permit is $525, which leaves $1,043 for catering. Vendor A at 110 meals is $1,045 - two dollars over. Vendor B's floor is $1,360, well over. Feeding 110 people is the minimum defensible quantity given 96 RSVPs plus a historical walk-in lift, so booking the DJ means under-catering the room on the night.
That is the binding constraint: every dollar of entertainment comes out of food, because the fixed costs and the reserve are not negotiable and the venue caps attendance at 140 regardless. The decision is not really entertainment versus no entertainment; it is entertainment versus enough food for the people who show up, and only one of those failures is recoverable in the moment.
2. The treasurer proposes covering the DJ by spending part of the $192 reserve. Give the strongest case for and against, then decide.
Read the worked answer
The case for is real: a DJ plausibly lifts attendance and makes the night feel like an event rather than a potluck, and the reserve is only $192 against a $2,400 budget - a small lever. If the council expects walk-ins to stay well under the cap, the marginal dollar arguably buys more atmosphere than it buys in extra plates.
The case against is stronger. The reserve exists for the things that only surface on the day: a custodial charge above the quote, a broken cable, an extra table rental, a last-minute supply run. Zeroing it converts a small, absorbable problem into an unfunded one. Second, running out of food is visible, unrecoverable during the event, and remembered; a phone playlist is merely unremarkable. Third, the 140-person cap limits the attendance upside the DJ is being bought to produce, so the return on the $525 is bounded at the top.
Decision: do not book the DJ. Use the center's house system and a curated playlist, keep the reserve intact, and if a surplus materializes afterward, spend it on the next event rather than this one.
3. Choose a caterer and a plate count. Show the arithmetic and address the timing problem.
Read the worked answer
Vendor B is eliminated on arithmetic before taste is discussed. A 200-plate minimum against a 140-person occupancy cap means paying for at least 60 plates that cannot legally be eaten, and $1,360 out of a $1,568 pool leaves $208 for everything else. The 72-hour flexibility is genuinely valuable, but it is bought at a price the budget cannot carry.
So: Vendor A. On quantity, 96 RSVPs with last year's roughly 15% walk-in lift projects about 110 attendees, and the trend is upward - 74 to 96 in four days. Order 120, the next multiple of ten above projection, for $1,140. That leaves $428. A $90 dessert tray brings food to $1,230 and leaves $338 of slack, plus the $192 reserve, comfortably above the 8% floor. Skip the permit and use the house speakers.
Handle the timing problem explicitly rather than pretending it away: Vendor A locks seven days out, so the order is placed before the RSVP count closes. The 120 figure is chosen so that being wrong in either direction is survivable - 20 plates of headroom under the 140 cap if turnout spikes, and roughly ten spare plates if it sags. Write the assumption and the lock date into the council minutes so the decision is auditable.