Optimisation

• How optimisation puzzles ask for best, minimum, or maximum outcomes under given rules.
• To translate "least cost", "maximum profit", "shortest path" into comparable numeric objectives.
• To combine logical constraints with candidate testing when formal algebra is not required.
• To solve Class 12 reasoning problems involving optimal assignment and resource limits.

Level 1 — Foundations

Verbal: Optimisation = find the best feasible solution, not any solution. Feasible means satisfies all constraints.

Steps:

1. Define objective (minimise distance, maximise score).
2. List constraints (budget, time, one-per-row rules).
3. Generate candidates (often finite in puzzles).
4. Compare objective values; pick optimum.

Types in exams:

Level 2 — Exam depth

Greedy caution: "Pick largest value first" may fail — always verify against constraints.

Bounds: Compute naive upper/lower bound to prune candidates (e.g. even if all remaining edges minimal, path > current best → stop).

Multi-objective: "Minimum cost with at least 2 doctors" — filter feasible set first, then minimise cost.

Integer restriction: People and seats are whole units — no fractional assignments.

Explain answer: State why no other feasible option beats yours — one-line comparison sufficient in subjective exams.

Minimum transport cost assignment

Three workers A,B,C to three jobs; costs:
        J1 J2 J3
    A   8  4  7
    B   5  9  6
    C   3  6  5
Each worker one job. Try small n exhaustive:
A-J2(4)+B-J1(5)+C-J3(5)=14; A-J1(8)+B-J2(9)+C-J3(5)=22; A-J2,B-J3,C-J1=4+6+3=13; A-J3,B-J1,C-J2=7+5+6=18.
Minimum **13** (A→J2, B→J3, C→J1).

Maximise score with cap constraint

Pick 3 projects from 5 with total hours ≤ 10; hours/scores given. List feasible triples under cap, compute score each, choose max — optimisation = filter then compare.

• Define feasible vs optimal in one line each.
• When is exhaustive search acceptable in exam puzzles?
• Greedy pick lowest cost job for each worker independently — why can it fail?
• Stretch: State objective for "maximum number of meetings in a day with no overlap."

Revision tip: Revisit adjacent topics in Advanced Puzzles before mixed practice on Optimisation.

Open the Practice tab for graded questions on Optimisation.

State the objective in one margin note (min cost, max score) before computing. For small assignment tables (n≤4), systematic enumeration is acceptable and reliable. After finding a candidate optimum, ask: Is there a cheaper feasible row swap? one time — catches many wrong greedy picks. Show one comparison line in written work for partial credit.

Optimisation sits beside constraint puzzles: first filter feasible set, then optimise objective. Percentage profit questions ask maximise revenue given discount caps — same compare-all-feasible pattern. Scheduling tables in analytical reasoning often hide optimisation ("earliest finish") — define objective before placing events. Learn to recognise when exhaustive search is feasible (n≤4 assignments) versus when elimination heuristics are required.