Allocating Six Students Across Three Programs Under a First-Choice-Full Rule
Bu Ratna advises six grade-12 students at a Surabaya high school who all want IUP UGM. From last cycle's published figures she builds a planning table. IUP Management: 60 seats, 690 eligible applicants. IUP Accounting: 40 seats, 520 eligible applicants. IUP Economics: 30 seats, 210 eligible applicants. This cycle the faculty announced that IUP Economics added 10 seats after a new laboratory opened, while the other two are unchanged. Applicant volumes are expected to be within 10% of last year.
Each student may submit two program choices. The portal considers only the first choice until that program is full, then moves to the second choice. The six students' profiles: two are strong in quantitative subjects with rapor mathematics above 90; three are balanced across subjects; one has an outstanding national debate record but mathematics at 75. All six meet the IELTS minimum. Bu Ratna wants to maximise the number of offers rather than the prestige of any single placement, and no student may apply to the same program twice.
1. Recompute the competitiveness of IUP Economics after the seat expansion and explain what that change should do to the group's planning.
Read the worked answer
Last cycle: 210 applicants ÷ 30 seats = 7.0 applicants per seat. After expansion: 210 ÷ 40 = 5.25 applicants per seat. Expressing the change both ways avoids a common error: seats rose by 33% (30 to 40), but the applicants-per-seat ratio fell by 25% ((7.0 − 5.25) ÷ 7.0), and only the ratio describes the applicant's odds.
Applying the ±10% volume assumption gives a range of 189 to 231 applicants, or 4.7 to 5.8 applicants per seat - still clearly the least crowded of the three (Management 11.5, Accounting 13.0). The planning consequence is that Economics is the only program where a second-choice placement is a realistic insurance policy, so it should absorb most second choices rather than being used as a prestige first choice by everyone.
The second consequence is subtler: if all six students route their second choice to Economics, they compete against each other for the same 40 seats. Spreading submissions across different waves, and checking whether the 10 new seats were added to Wave 2 or Wave 3, matters as much as the ratio itself.
2. Propose a first-choice and second-choice allocation for the six students and justify the logic, given that a second choice is only read once the first-choice program is full.
Read the worked answer
Allocation logic: match first choices to the profile dimension the program actually rewards, then use Economics as the shared fallback.
First choices: the two quantitative students go to Accounting and Economics (not both to Accounting - the 13.0 ratio means one of them is likely to be displaced, and their mathematics profile is the strongest asset in a quantitative pool). The three balanced students go one to Management, one to Accounting, one to Economics, spreading the risk so that the group is not concentrated in a single 60-seat program with 11.5 applicants per seat. The debate student goes to Management, where a 30% interview component lets an exceptional oral record offset a mathematics score of 75.
Second choices: everyone whose first choice is Management or Accounting lists Economics, because it is the only program with a materially better ratio. The student whose first choice is already Economics lists Management as a second choice, since a second choice identical to a first choice is not permitted.
The key structural point is that a second choice is dormant until the first-choice program fills. So the allocation must be justified primarily on first-choice plausibility, with Economics functioning as a genuine safety net rather than a real preference for most of the group.
3. Identify the assumptions that could invalidate this plan and rank them by how much damage each would cause.
Read the worked answer
Most damaging: the assumption that the first-choice program will still be accepting applications in the wave the student targets. Seats are filled wave by wave, so a program can close before the second choice is ever read - in that case the Economics safety net is worthless and the plan collapses. Before paying, each student should confirm in writing whether the target program closed early in previous cycles.
Second: the definition of 'eligible applicants.' If the published 690 and 520 were post-screening figures and this cycle's screening is stricter or looser, the ratios shift without any change in seat count.
Third: the ±10% volume assumption. A single viral post or a new scholarship can move a program's applicant count well beyond 10% in one cycle, and capacity is fixed.
Fourth: the implicit assumption that seats are the only constraint. Teaching capacity, laboratory slots and accreditation ratios can cap admissions below the announced number.
Least damaging but still relevant: the assumption that the students' IELTS scores remain valid through the deadline, and that none of them withdraws after an offer, which would free a seat that the plan does not count on.