Solved Assignments 1β10
All 53 problems from the ten QT assignments, each solved step by step with the method that solves it, the shortcut that saves time, and a link to the theory.
Every assignment page has the same shape: a method card, a tricks card, then each problem as Question β numbered solution steps β final answer. The original assignment opens in the side viewer from the button in each page's header bar.
The ten assignments
| # | Assignment | Unit | Problems | Core method | Exam question it prepares you for |
|---|---|---|---|---|---|
| 1 | LPP formulation & graphical | Unit 1 | 6 | Four blocks; corner-point table | Q3B (5) both papers |
| 2 | LPP special cases | Unit 1 | 8 | Final simplex table β four signals | Q7A / Q7B (5) |
| 3 | Sensitivity analysis | Unit 1 | 4 | Rule β number β arithmetic β meaning | Q4A / Q4B (5) both papers |
| 4 | Duality | Unit 1 | 5 | Canonical form, split equalities | Q1A (2.5) both papers |
| 5 | Queuing (M/M/1) | Unit 5 | 5 | Ξ», ΞΌ per hour β Ο β six formulas | Q5A (5) both papers |
| 6 | Assignment & transportation | Unit 3 | 5 | Cost matrix, balance, mΓn and m+n | Q1B (2.5), Q5B, Q7 (5) |
| 7 | Game theory & AHP | Units 4, 7 | 5 | Payoff matrix + saddle point; normalise & average | Q3A (5), Q1C (2.5) |
| 8 | Decision theory | Unit 7 | 7 | Five criteria; EMV/EVPI; trees | Q1D (2.5), Q6A, Q6B (5) |
| 9 | Simulation | Unit 6 | 4 | RN ranges 00β99, day-by-day table | Q2 (10) both papers |
| 10 | Integer programming | Unit 2 | 4 | Binary y, link x β€ capΒ·y, logic constraints | Q4A / Q4B (5) both papers |
Every number on these pages was re-computed independently β the LPs by an exact simplex solver, the queues, trees and simulations by direct calculation β before being written up.
Which method? β read the question, pick the tool
| If the question says⦠| It is⦠| Go to |
|---|---|---|
| "formulate the LPP", resources, profit/cost per unit | LP formulation | A1 |
| a final simplex table, "identify the special case" | Special cases | A2 |
| a table with Reduced cost / Dual value / LowerβUpper bound | Sensitivity analysis | A3 |
| "convert the primal to its dual" | Duality | A4 |
| arrival rate, service time, Poisson / exponential | Queuing M/M/1 | A5 |
| flights to pair, workers to tasks / plants to markets | Assignment / transportation | A6 |
| two competing firms, "payoff represents X's advantage" | Game theory | A7 |
| pairwise comparisons on a 1β9 scale | AHP | A7 |
| states of nature, payoffs, optimism/pessimism, Ξ± | Decision under uncertainty | A8 |
| probabilities of states, "survey", "decision tree" | EMV / decision tree | A8 |
| probability distribution + list of random numbers | Simulation | A9 |
| "which to open / select", fixed cost, ifβthen conditions | Integer programming | A10 |
Errors found in the handouts, keys and slides
Read these before you revise from the originals
- A3 Q1 β Constraint 4's slack is printed "45"; it is 0.45 (the report column is truncated). β
- A3 Q3 β C3 is printed Xβ + Xβ β€ 15, but the report only fits 3Xβ + Xβ β€ 15. β
- A7 Game Q2 β strategy H is written "A" in two sentences and payoffs are phrased loosely; the reading used is stated. β
- A8 Q4 β the conditional probabilities imply P(High) = 0.32, not the 0.35 printed; solved as given. β
- A9 Q1 β "fewer than 303" should be fewer than the container's 305. β
- A10 Q3 β the conditions plus the βΉ120 lakh budget admit no feasible selection. β
- A10 Q4 β condition 3 reads "P2 and P2"; three readings are solved. β
- Final Q5B key β cells in rows 902, 903, 904 of the idle-time matrix are wrong; checked values in A6 Q3.
- Re-Exam Q2 key β carries the backlog on day 2 but drops it on days 3β5; average waiting should be 0.6, not 0.2. β
- Re-Exam Q6B key β uses the Final paper's numbers; with the Re-Exam's own data the Hurwicz choice is U1 (138), not U3. β
- Lecture p. 17 β EOL of S2 is 3, not 7.5 (least EOL must equal EVPI = 3). β
How to use these pages in the last week
- Read the method card at the top of an assignment β it is the whole technique in four or five lines.
- Cover the solution and attempt one problem on paper; then compare step by step.
- Do the 10-mark simulation (A9) and the decision trees (A8) at least once by hand β they are the longest answers on the paper.
- Finish with the Solved Papers: every 2025-26 question now has a model answer.