ETF2480 Optimisation for Business
The Complete Exam Bible · S2 2026ETF2480 Overview
- Semester 2 2026
- Monash University
- Level 2
- Mathematical optimisation
ETF2480 Optimisation for Business develops the skill of turning a managerial decision into a mathematical model, solving that model and explaining what the result means.
- Assessment focus The final exam contributes half of the unit result.
- Core method Define, formulate, solve, verify and interpret.
- Model families Linear, network and integer optimisation.
- Best revision move Explain every coefficient and constraint direction.
What you get in the full ETF2480 Exam Bible
- 8 chapters, 44 pages — every examinable topic, week by week
- 32 original practice questions, each with a model answer in the Final Exam format
- 8 worked examples, solved the way ETF2480 marks
- 17 computed figures, redrawn from the course’s own numbers
- Exam-morning plan for the Final Exam (50%) — what to revise last, where marks are lost
Free on this page: assessment table, chapter map, one worked example, key terms, FAQ. The rest is in the full exam bible.
How ETF2480 is assessed
| Component | Weight | Format |
|---|---|---|
| Assignment 1 | 15% | Individual assessment due in Week 4; mathematical formulation, numerical solution and interpretation |
| Mid Semester Test | 20% | Individual test in Week 6 |
| Assignment 2 | 15% | Individual assessment due in Week 10 |
| Final Exam | 50% | Individual assessment in the final exam period; check the current Moodle notice for duration, sections, question types and permitted materials |
The published weights total 100%. The unit outline directs hurdle requirements to the Handbook; verify the current rule in the 2026 Handbook and Moodle assessment notice.
What other students are asking about ETF2480
- Where can I find lecture notes or study guides for ETF2480 at Monash?
- The ETF2480 study guide in AskSia Library covers Optimisation for Business in 8 chapters, with the assessment table, a chapter-by-chapter topic map, key terms and a worked example, free to read on this page.
- Is there a final exam in ETF2480, and how much is it worth?
- Yes. In the offering this AskSia Library guide is built from, Final Exam carries 50% of the ETF2480 mark; the full split is Assignment 1 15%, Mid Semester Test 20%, Assignment 2 15%, Final Exam 50%.
- What does ETF2480 cover on feasible regions and optimal solutions?
- In AskSia Library's ETF2480 guide, the Feasible Regions and Optimal Solutions chapter explains feasible geometry, extreme points, alternate optima and solver status.
- What does ETF2480 cover on business applications of linear programs?
- In AskSia Library's ETF2480 guide, the Business Applications of Linear Programs chapter explains blending, multi-period inventory, investment and process conservation.
- What does ETF2480 cover on duality and sensitivity analysis?
- In AskSia Library's ETF2480 guide, the Duality and Sensitivity Analysis chapter explains primal-dual bounds, shadow prices, complementary slackness and valid ranges.
Current ETF2480 dates
| Date | Item | Control |
|---|---|---|
| 2026-08-21 | Assignment 1 due | Friday at 11:55 PM |
| 2026-10-07 | Assignment 2 due | Wednesday at 11:55 PM |
Dates come from the Semester 2 2026 Moodle assessment page. Confirm exact deadlines and submission settings in the live LMS.
What ETF2480 covers
Follow the optimisation workflow from linear models and feasible regions through duality, networks, discrete decisions and exact search.
Linear Programming Model Anatomy
Decision variables, objectives, constraints, domains and matrix formLinear programming begins with translation.
- Decision variables and units
- Linear objectives and coefficient meaning
- Capacity, demand and balance constraints
- Non-negativity and variable domains
- Matrix form cTx and Ax <= b
- Equivalent max, min and inequality transformations
Feasible Regions and Optimal Solutions
Feasible geometry, extreme points, alternate optima and solver statusA feasible region contains every decision that satisfies all constraints. In two dimensions, each inequality keeps one side of a line and their intersection forms a polygon or another convex set.
- Half-planes and feasible intersections
- Extreme points and objective contours
- Unique and alternate optima
- Infeasible constraint systems
- Unbounded improving directions
- Status-first solver interpretation
Business Applications of Linear Programs
Blending, multi-period inventory, investment and process conservationMany business linear programs share a conservation structure. Blending models total attributes contributed by ingredients and enforce composition bands.
- Diet and blending requirements
- Multi-period inventory balance
- Cash and investment timing
- Production-process conservation
- Yield and conversion coefficients
- Initial and terminal conditions
Duality and Sensitivity Analysis
Primal-dual bounds, shadow prices, complementary slackness and valid rangesDuality pairs an LP with another optimisation problem that exchanges the roles of rows and columns. Primal constraints create dual variables, primal variables create dual constraints, and the coefficient matrix is transposed.
- Primal and dual correspondence
- Weak and strong duality
- Resource bounds and dual values
- Complementary slackness
- Shadow-price units
- Allowable ranges and basis changes
Transportation and Assignment Networks
Node balance, supply and demand, dummy nodes and one-to-one matchingTransportation models allocate flow from supply nodes to demand nodes. Each arc carries a shipment decision and unit cost, while source and destination rows enforce the published totals. Balanced models have equal aggregate supply and demand.
- Source and destination indices
- Supply and demand balance
- Balanced and unbalanced transport
- Dummy nodes and penalties
- One-to-one assignment
- Network integrality and side constraints
Shortest Paths and Maximum Flow
Route cost, directed conservation, arc capacity and bottleneck cutsShortest path and maximum flow share directed networks and node conservation but answer different questions. A shortest-path model sends one unit from source to sink and minimises total arc length, time or cost.
- Directed arcs and reachability
- Source, intermediate and sink balance
- Shortest-path objective
- Maximum-flow capacity
- Source-to-sink cuts
- Bottleneck interpretation
Integer Programming Formulations
Binary logic, fixed charges, coverage, facility links and LP relaxationInteger programming represents decisions that cannot be divided freely. Binary variables model opening, selecting, assigning and activating. General integer variables count indivisible units, while continuous variables can coexist in a mixed-integer model.
- Binary and general integer domains
- Fixed-charge decisions
- Logical implication rows
- Facility location and coverage
- LP relaxation bounds
- Big-M strength and units
Branch-and-Bound and Stronger Models
Incumbents, bounds, pruning, cutting planes and formulation strengthBranch-and-bound solves an integer program by repeatedly solving LP relaxations, branching on fractional decisions and pruning subproblems that cannot improve the best feasible integer solution.
- Relaxation bounds
- Incumbents and feasible values
- Branching on fractional variables
- Infeasibility and bound pruning
- Valid cutting planes
- Strong versus weak formulations
The Semester 2 unit begins with linear programming: decision variables, objectives, resource constraints, feasible regions and matrix form for implementation in R or Python.
It then moves through recurring business applications such as blending, multi-period production and process models before using duality and sensitivity analysis to value scarce resources and test how far a recommendation remains valid.
The second half uses networks and discrete decisions. Transportation and assignment models express supply, demand and one-to-one matching through node balance.
Shortest-path and maximum-flow models distinguish a single route from total throughput. Integer programming introduces binary choices, fixed charges, logical implications, facility location and coverage.
Branch-and-bound, cutting planes and stronger formulations explain how exact solvers search efficiently and certify solution quality.
The official assessment structure places substantial weight on both coursework and the final exam.
Strong answers do more than present solver output: they define variables with units, justify each constraint, check status and feasibility, report the objective and decision values in context, and identify limitations. This guide uses original questions and new data while following the model families and reasoning roles in the Monash materials.
Worked example · free
Formulate and solve a two-product capacity decision
- +1Define x and y as standard and premium kits, then maximise 36x + 54y.
- +2Write 2x + 3y <= 90 for cutting, x + 3y <= 66 for finishing, and x,y >= 0.
- +2Solve the binding equations to obtain x = 24 and y = 14; profit is 36(24) + 54(14) = $1,620.
- +1Report that both capacities bind and the conclusion assumes divisible output and the stated unit contributions.
Key terms
- Decision variable
- A controllable quantity whose value the optimisation model chooses.
- Objective function
- The linear or nonlinear expression the model maximises or minimises.
- Feasible region
- The set of decisions satisfying every constraint and variable domain.
- Binding constraint
- A constraint met at equality by the reported solution.
- Dual problem
- The paired optimisation problem that provides bounds and values for primal constraints.
- Shadow price
- The local objective change per unit change in a constraint right-hand side within its valid range.
- Flow balance
- A node equation reconciling inflow, outflow and any stated supply or demand.
- Assignment model
- A unit transportation model that matches each agent to one task and each task to one agent.
- Binary variable
- A decision variable restricted to zero or one for a yes-or-no choice.
- LP relaxation
- A continuous model formed by removing integer restrictions from an integer program.
- Incumbent
- The best feasible integer solution currently known during an exact search.
- Cutting plane
- A valid inequality that removes fractional relaxation points while retaining all feasible integer solutions.
ETF2480 FAQ
What makes Optimisation for Business challenging?
The main difficulty is formulation rather than arithmetic. You must translate business language into variables, objectives, balances, bounds and logical links, then interpret solver output without overstating it. A model can run successfully while representing the wrong decision, so units, status, feasibility and contextual conclusions all matter.
How is the unit assessed?
The Semester 2 structure is Assignment 1 at 15%, a Mid Semester Test at 20%, Assignment 2 at 15% and a Final Exam at 50%. All four rows are individual assessments in the official outline. Check Moodle for current task instructions and the Handbook for the applicable hurdle rule.
What is published about the final exam?
The official outline identifies an individual Final Exam worth 50% in the final exam period. The captured unit files used for this guide do not supply the duration, section structure, question types or permitted materials, so use the current Moodle examination notice for those operational details.
Do I need R or Python?
The learning outcomes require implementation in scalable software, and the lectures demonstrate both R and Python formulations. Learn how variable order, objective coefficients, constraint matrices, directions and right-hand sides map into code. Always inspect solver status and translate the returned vector back into named decisions.
How should I practise formulation?
Start by defining variables with units, then label the objective and each family of constraints. Read every equation back as a business sentence, test simple feasible and infeasible plans, and check coefficient dimensions. Finish by explaining the decision vector, objective value, binding limits and a relevant modelling assumption.
Why are duality and sensitivity useful?
Duality supplies bounds and resource values, while sensitivity analysis asks how an optimum changes when model data move. Shadow prices are local statements tied to a specific right-hand side and validity range. They help value capacity changes, but they must not be extrapolated beyond the reported interval.
How do network models differ?
Transportation allocates flow from supply to demand, assignment creates one-to-one matches, shortest path chooses one minimum-cost route, and maximum flow sends the greatest total throughput under capacities. Their shared language is node balance, but the objective and source-to-sink requirements distinguish the models.
Why can I not round an LP relaxation?
Independent rounding can violate constraints or produce a weak discrete decision. The relaxation is valuable because it provides a bound, not because its fractional solution is automatically implementable. Use an integer model and an exact or justified approximate method when decisions must be discrete.
Questions students ask in each ETF2480 chapter
- How do I choose decision variables?
- Identify the choices management directly controls, then define each with a noun, time period, unit and index when needed. Avoid variables that are merely outputs of the decision unless they simplify the model and are linked by a defining equation. Chapter 01 · Linear Programming Model Anatomy
- Why do linear optima occur at corners?
- A linear contour moves across a convex polygon without bending. Its final contact in the improving direction includes an extreme point, although an entire edge can tie when the contour is parallel to that edge. This result supports vertex checking only for small graphical models. Chapter 02 · Feasible Regions and Optimal Solutions
- How do blending percentages stay linear?
- When total blend mass is fixed, attribute contribution is a weighted sum bounded by fixed requirements. If total mass varies, a percentage condition can often be written with the required proportion multiplied by total quantity on the other side, which remains linear after collecting terms. Chapter 03 · Business Applications of Linear Programs
- What does the dual represent?
- It assigns values to primal constraints and creates a bound on the primal objective. In a resource model, those values can describe local marginal worth, but their exact interpretation depends on objective units, row units and the current optimal basis. Chapter 04 · Duality and Sensitivity Analysis
- How do I balance excess supply?
- Add a dummy destination whose demand equals the excess. Its arc cost should represent genuine non-use, disposal or storage consequences. A zero cost is defensible only when sending flow to the dummy has no relevant effect. Chapter 05 · Transportation and Assignment Networks
- What is the main difference between path and flow?
- A shortest path selects one route for a unit and minimises total weight. Maximum flow maximises a total quantity that may divide across several routes and recombine. The source and sink equations therefore contain different objective logic. Chapter 06 · Shortest Paths and Maximum Flow
- Why is rounding a relaxed solution unsafe?
- Rounding variables independently can break capacity, balance, coverage or logical rows. Even a feasible rounded plan may be far from the best integer solution. Treat the relaxation objective as a bound and solve the discrete model when indivisibility matters. Chapter 07 · Integer Programming Formulations
- Why does branching preserve all integer options?
- If an integer variable has fractional value 3.7, one child restricts x to at most 3 and the other restricts x to at least 4. They cover every integer possibility while excluding the current fractional point, so together they partition the relevant integer search without losing a feasible discrete value. Chapter 08 · Branch-and-Bound and Stronger Models
How to study for the exam
Organise revision around the modelling cycle. First, practise translating nouns into indexed variables and units. Second, write constraints by role: capacity, balance, demand, coverage or logic. Third, solve only after you can explain every row, then inspect status and substitute the decision back into the model.
Fourth, report the objective and decision vector in business language, including the binding resource, relevant sensitivity range or modelling limitation. Compare nearby model families so the structural distinction becomes automatic: blend versus time balance, transportation versus assignment, shortest path versus maximum flow, and LP relaxation versus integer solution.
Use the solved mid-semester practice set to identify question types, but complete fresh problems with new data so you are learning the method rather than a particular stem. Before the final exam period, confirm the published examination format and permitted materials on Moodle because the captured outline establishes the weight and timing but not those mechanics.
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