The School Festival Budget and the Missing Sponsor
A student council at a Polish secondary school is planning a one-day school festival. The confirmed budget is 4,800 PLN. A local bakery promised 600 PLN but has not signed anything. Ticket sales are expected to bring in between 2,000 and 3,000 PLN, depending on weather. Fixed costs already contracted: sound system rental 1,200 PLN, decorations 700 PLN, and insurance 400 PLN. The council also wants to fund a guest speaker who charges 1,500 PLN plus travel of 300 PLN. Two weeks before the event, the weather forecast shows a 40% chance of heavy rain, which would cut ticket sales to the lower estimate. The principal says the event cannot run at a loss under any scenario. The council must decide whether to invite the speaker now or wait.
1. Using the pessimistic scenario (no bakery money, rain, lowest ticket sales), determine whether the council can afford the guest speaker. Show your arithmetic.
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Worst-case income: tickets 2,000 PLN + bakery 0 PLN = 2,000 PLN. Worst-case costs without the speaker: 1,200 + 700 + 400 = 2,300 PLN. That already produces a deficit of 300 PLN before the speaker is considered. Adding the speaker (1,500 + 300 = 1,800 PLN) gives total costs of 4,100 PLN against 2,000 PLN income - a loss of 2,100 PLN. Even the confirmed 4,800 PLN budget does not rescue this: if we treat 4,800 as available cash, 4,800 + 2,000 = 6,800 PLN available, minus 4,100 PLN costs = 2,700 PLN surplus; but the 4,800 is the whole budget, not spare cash, and the principal's rule is about the event not running at a loss, so the honest reading is that the speaker cannot be committed under the pessimistic scenario without a guaranteed income source. The conclusion: do not sign the speaker yet.
2. The council wants a decision rule that satisfies the principal under every scenario. Propose one and justify it in terms of risk.
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A sound rule is: commit to the speaker only when guaranteed (contracted) income covers all fixed costs plus the speaker fee plus travel, with a safety margin. Guaranteed income here is the 4,800 PLN budget (if it is genuinely uncommitted) - the bakery's 600 PLN is not guaranteed and ticket sales are uncertain. Costs with the speaker are 4,100 PLN, leaving 700 PLN margin; that is thin but positive. However, if any part of the 4,800 PLN is already earmarked, the margin disappears. So the rule should require a signed bakery agreement or a written ticket pre-sale figure before signing. This converts an uncertain bet into a bounded risk: the downside is capped at losing the speaker deposit, not the whole event.
3. The bakery finally offers a signed contract but only for 300 PLN. Does this change your recommendation? Explain.
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It improves the guaranteed floor by 300 PLN but does not change the structural problem: the pessimistic ticket scenario still leaves the event short. With 4,800 + 300 = 5,100 PLN guaranteed and costs of 4,100 PLN, the margin is 1,000 PLN - better, but the 40% rain risk still threatens the ticket line. The recommendation stands: the signed 300 PLN helps, yet the council should either secure pre-sales or trim the speaker's travel cost (for example, a local speaker) before committing. The judgement being tested is that a partial guarantee reduces but does not eliminate risk.