The Campaign Budget That Wouldn't Balance
A student council has a fixed budget of ₱12,000 for an awareness campaign. Printing a tarpaulin costs ₱350 per piece, and the print shop charges a one-time ₱1,200 layout fee regardless of how many tarpaulins are ordered. Campaign shirts cost ₱180 each, but the supplier accepts orders only in bundles of 6. Council rules require at least 8 tarpaulins and require that 10% of the total budget be held back as a contingency reserve that cannot be spent on either item. At the final meeting, one officer proposes ordering 12 tarpaulins "since the design fee is already paid," and another proposes dropping the reserve because "nothing has gone wrong so far." The treasurer must present a defensible purchase plan to the adviser.
1. Under the council rules, what is the maximum number of shirt bundles the treasurer can order, and how much money is left unspent?
Read the worked answer
Step 1 - Reserve first. 10% × ₱12,000 = ₱1,200 locked. Spendable = ₱12,000 − ₱1,200 = ₱10,800.
Step 2 - Tarpaulins at the minimum. The rule is at least 8, and every extra tarpaulin costs real money in shirts, so check the minimum first: 8 × ₱350 = ₱2,800, plus the one-time ₱1,200 fee = ₱4,000.
Step 3 - Shirts. ₱10,800 − ₱4,000 = ₱6,800. One bundle = 6 × ₱180 = ₱1,080.
Step 4 - Round down, not to nearest. 6,800 ÷ 1,080 = 6.29 → 6 bundles (₱6,480). A 7th bundle would cost ₱7,560 > ₱6,800.
Answer: 6 bundles (36 shirts); ₱6,800 − ₱6,480 = ₱320 unspent.
2. Evaluate the officer's proposal to order 12 tarpaulins. How many shirt bundles are lost, and does the "design fee is already paid" argument justify the change?
Read the worked answer
Cost of the 12-tarpaulin plan: 12 × ₱350 = ₱4,200, plus ₱1,200 = ₱5,400. Remaining = ₱10,800 − ₱5,400 = ₱5,400. Bundles = 5,400 ÷ 1,080 = exactly 5.
Trade-off: 6 bundles → 5 bundles, so 6 shirts are sacrificed for 4 extra tarpaulins. Leftover cash drops from ₱320 to ₱0.
On the argument itself: it is a sunk-cost error. The ₱1,200 fee appears in both plans, so it cancels out and cannot favour either one. The true marginal cost of one more tarpaulin is ₱350, not ₱350 plus a share of the fee.
Defensible framing: the question is not whether the fee is paid but whether 4 additional tarpaulins deliver more value than 6 shirts. If the officer cannot show that, the 8-tarpaulin plan is the better use of the same budget.
3. A second officer proposes spending the ₱1,200 reserve on one extra shirt bundle. Quantify what the council gains and what it gives up, and give a recommendation.
Read the worked answer
What is gained: ₱1,080 buys 1 more bundle = 6 shirts, roughly a 17% increase over 36 (6/36 ≈ 17%). About ₱120 would remain.
What is given up: the entire contingency buffer - 10% of the budget goes to zero. Any single unplanned peso (a reprinted tarpaulin at ₱350, transport, a damaged shirt) then has no legal source of funds under the council's own rule.
Judgement: the gain is small and linear (6 shirts); the loss is the ability to absorb any shock, which is unbounded in principle and, in this setup, larger than the ₱1,080 being spent (one reprint already exceeds the ₱120 leftover).
Recommendation: reject the proposal, or restate it honestly as a rule change requiring adviser approval - not as a purchase decision. The "nothing has gone wrong so far" reasoning is precisely the argument the reserve exists to defeat.