Ration and Transport Plan for a 42-Candidate Study Camp
A PMA aspirant is asked to plan one Saturday for 42 candidates travelling from a study academy to a camp 18 km away. Two coasters are available: Coaster A seats 26 and costs PKR 9,600 for the round trip; Coaster B seats 18 and costs PKR 7,200. A 52-seat bus costs PKR 14,000, but it must leave 25 minutes earlier than the coasters and cannot wait beyond 4:10 p.m. The camp starts at 8:30 a.m. Loading takes 15 minutes, travel takes 30 minutes, and a security stop takes 10 minutes. The group must return by 4:30 p.m. and must have a full 5-hour camp. No vehicle may be overloaded. Ration is budgeted at PKR 21,000 for 42 packs costing PKR 480 each; the vendor gives 10% off only if at least 40 packs are ordered by Thursday. The candidate must choose the lowest-cost transport that moves all 42 people in one movement and check whether the ration budget is sufficient.
1. Which transport option is feasible and cheapest? Show capacity, timing, and cost.
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Capacity: A alone carries 26 and B alone carries 18, so neither alone can move 42. A + B carry 44 at a cost of PKR 9,600 + 7,200 = PKR 16,800. The bus carries 52 at PKR 14,000.
Timing: one-way time is loading 15 min + travel 30 min + security 10 min = 55 min. To start at 8:30 a.m., the coasters must leave at 7:35 a.m. The bus leaves 25 min earlier at 7:10 a.m. and arrives at 8:05 a.m., so it is not late. A full 5-hour camp ends at 1:30 p.m.; the return journey takes 55 min, so the group is back by about 2:25 p.m., well before 4:30 p.m. The bus also leaves before its 4:10 p.m. waiting limit.
Decision: the bus is feasible and cheapest because PKR 14,000 is less than PKR 16,800, and it has enough seats. A + B is the backup option.
2. If the bus is unavailable, what is the next cheapest feasible choice, and how much ration budget remains with and without the discount?
Read the worked answer
If the bus is unavailable, the only feasible single-movement choice is A + B: capacity 44 is at least 42, cost PKR 16,800. Ration cost at full price is 42 × PKR 480 = PKR 20,160. With the 10% discount it is PKR 20,160 × 0.90 = PKR 18,144. Against the PKR 21,000 budget, the surplus is PKR 21,000 − 18,144 = PKR 2,856 with the discount, and PKR 21,000 − 20,160 = PKR 840 without it. Both are within budget, but the Thursday order is worth PKR 2,016 in savings.
3. A 43rd candidate joins after booking. Does the transport decision change? Explain.
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No, the bus remains the cheapest feasible option: it seats 52, so 43 is still within capacity and the cost stays PKR 14,000. If the bus is unavailable, A + B still works because capacity 44 can carry 43, leaving one spare seat, and the cost remains PKR 16,800. Ration for 43 packs is 43 × PKR 480 = PKR 20,640; with 10% discount it is PKR 18,576, leaving PKR 2,424 from the PKR 21,000 budget, and without discount it leaves PKR 360. A 45th candidate would change the decision because A + B would be over capacity; then the bus, or an extra vehicle, would be required.