ETF5248 Optimisation for Business
The Complete Exam Bible · S2 2026ETF5248 Overview
- Monash University
- Semester 2 2026
- Postgraduate level unit
- Optimisation and business modelling
- Seven teaching topics
- Quantitative assessment focus
ETF5248 Optimisation for Business is a postgraduate Monash University unit about turning business decisions into mathematical models that can be solved, checked and explained.
- Assessed by Two individual assignments worth 15% each, a 20% mid-semester test and a 50% final examination. The published components sum to 100%.
- Hardest step Translating a business rule into the correct variables, constraint direction, domain and linking logic before asking a solver for an answer.
- How to prepare Formulate each model from a blank page, solve representative numbers, then audit feasibility, units, bounds and managerial meaning without relying on the solver status alone.
What you get in the full ETF5248 Exam Bible
- 7 chapters, 35 pages — every examinable topic, week by week
- 23 original practice questions, each with a model answer in the Final Examination format
- 7 worked examples, solved the way ETF5248 marks
- 12 computed figures, redrawn from the course’s own numbers
- Exam-morning plan for the Final Examination (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 ETF5248 is assessed
| Component | Weight | Format |
|---|---|---|
| Assignment I | 15% | Individual artefact scheduled in Week 4, due 21 August 2026, with a separate R or Python file submission. |
| Mid Semester Test | 20% | Individual core-competency test scheduled in Week 6. |
| Assignment II | 15% | Individual artefact scheduled in Week 10, due 7 October 2026, with a separate R or Python file submission. |
| Final Examination | 50% | Individual core-competency examination in the final examination period, assessing the published unit learning outcomes. |
The Monash Handbook groups the assessment as artefacts worth 30%, a quiz or test worth 20%, and an examination worth 50%. The Semester 2 unit materials resolve the artefact component into Assignment I and Assignment II at 15% each. No hurdle is stated for these four components in the acquired sources. The source confirms the final examination weight and role, but does not state its duration, sections, question types or permitted materials, so those details must be checked in official examination instructions when released.
Assessment structure
Segment widths reproduce the four published Semester 2 weights, which total 100%.
What other students are asking about ETF5248
- Where can I find lecture notes or study guides for ETF5248 at Monash?
- The ETF5248 study guide in AskSia Library covers Optimisation for Business in 7 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 ETF5248, and how much is it worth?
- Yes. In the offering this AskSia Library guide is built from, Final Examination carries 50% of the ETF5248 mark; the full split is Assignment I 15%, Mid Semester Test 20%, Assignment II 15%, Final Examination 50%.
- What does ETF5248 cover on business models with linear programming?
- In AskSia Library's ETF5248 guide, the Business Models with Linear Programming chapter explains multi-period inventory balances · blending and recipe constraints · product mix · managerial interpretation.
- What does ETF5248 cover on duality and sensitivity analysis?
- In AskSia Library's ETF5248 guide, the Duality and Sensitivity Analysis chapter explains primal and dual structure · shadow prices and slack · allowable ranges · evidence-led recommendations.
- What does ETF5248 cover on network flow models?
- In AskSia Library's ETF5248 guide, the Network Flow Models chapter explains nodes, arcs and conservation · shortest path and maximum flow · transportation and assignment · cut checks.
Current ETF5248 dates
| Date | Item | Control |
|---|---|---|
| 21 August 2026 | Assignment I due | Week 4 individual artefact, worth 15%, with a separate R or Python file submission. |
| Week 6 | Mid Semester Test | Individual core-competency assessment worth 20%. |
| 7 October 2026 | Assignment II due | Week 10 individual artefact, worth 15%, with a separate R or Python file submission. |
| Final examination period | Final Examination | Individual core-competency assessment worth 50%; consult official instructions for format and permitted materials. |
Dates are as published in the Semester 2 2026 Unit Schedule and Assessment Summary and the unit assessment pages. Confirm exact deadlines and submission settings in the live LMS.
What ETF5248 covers
The unit starts with linear programming and business formulations, then develops duality, sensitivity and network flow before moving to integer, piecewise and convex optimisation. The final review connects each business cue to the model family and validation check it requires.
Linear Programming Foundations
decision variables and objective functions · constraint direction and domains · feasible regions and corner points · formulation checksLinear programming turns a decision into variables, an objective, linear constraints and domains. The formulation must preserve both the business meaning and the units of every quantity.
- Decision variables with units and domains
- Maximisation and minimisation objectives
- Capacity, requirement and balance constraints
- Feasible regions and corner points
- Binding rows, slack and resource use
- Infeasible, unbounded and alternative solutions
Business Models with Linear Programming
multi-period inventory balances · blending and recipe constraints · product mix · managerial interpretationBusiness linear programs often repeat a small number of structures.
- Multi-period inventory balance equations
- Initial and terminal boundary conditions
- Production, holding and shortage costs
- Blending variables with two indices
- Availability, output and recipe rows
- Product mix and whole-unit cautions
Duality and Sensitivity Analysis
primal and dual structure · shadow prices and slack · allowable ranges · evidence-led recommendationsDuality gives each primal constraint an economic price and each primal variable a corresponding dual restriction.
- Primal rows and dual variables
- Primal variables and dual constraints
- Weak and strong duality
- Complementary slackness
- Shadow prices and resource values
- Allowable ranges and local interpretation
Network Flow Models
nodes, arcs and conservation · shortest path and maximum flow · transportation and assignment · cut checksNetwork models describe movement through nodes and directed arcs. A variable records flow on an arc, capacity limits that flow, and conservation reconciles inflow, outflow, supply and demand at each node.
- Nodes, directed arcs and capacities
- Flow conservation at transshipment nodes
- Shortest path and minimum cost
- Maximum flow and source-sink value
- Cuts as optimality checks
- Transportation and assignment structures
Integer Programming Decisions
binary logic and fixed charges · linking constraints · branch and bound · incumbent and gap interpretationInteger programming represents choices that cannot be divided continuously. Binary variables encode open or closed, selected or rejected, and logical states, while general integers represent countable quantities.
- Binary and general integer domains
- Fixed charges and activation logic
- Tight linking bounds
- Covering, knapsack and facility patterns
- LP relaxation and branch and bound
- Incumbents, bounds, pruning and gaps
Piecewise and Convex Optimisation
segment variables and breakpoints · tier logic · convex sets and functions · global optimality checksAdvanced business models often contain changing marginal rates or smooth curvature.
- Piecewise-linear marginal rates
- Segment capacities and ordered fill
- All-units tiers and binary logic
- Breakpoint and continuity checks
- Convex sets and convex functions
- Local and global optimality
Model Selection and Exam Review
business cues and model families · formulation workflow · solver-output audit · timed review practiceThe final review is about choosing and defending a model, not attaching a memorised formula to a keyword.
- Business cues and model families
- Variable, objective and constraint workflow
- Domain and logic checks
- Independent solver-output audit
- Sensitivity and limitation statements
- Timed mixed-model review
It begins with linear programming: define variables, construct a measurable objective, translate scarce resources and requirements into constraints, specify the domain, and interpret a feasible optimum. The geometry matters because a two-variable feasible region makes constraint direction, binding rows and corner-point optimality visible. The unit then moves from a generic linear model to recurring business patterns.
Multi-period planning uses balance equations to connect opening stock, production, demand and closing stock. Product-mix and blending models separate resource availability, output definitions and quality rules so every coefficient has a physical meaning. Duality and sensitivity analysis add an economic layer.
A shadow price values one extra unit of a binding resource, slack identifies unused capacity, and allowable ranges state when a local interpretation remains valid. Network flow gives a specialised language for movement through nodes and arcs. Shortest-path, maximum-flow, transportation and assignment models all rely on conservation, but their objectives and capacities differ.
Integer programming is needed when decisions are indivisible or logical, such as opening a facility, choosing a project or enforcing an either-or condition. Binary linking constraints and branch-and-bound bounds turn a discrete answer into a proof. The advanced topic distinguishes piecewise-linear costs from convex optimisation.
Segment variables preserve tariffs with changing marginal rates, while convexity can certify that a local minimum is global when the objective and feasible set have the required shape. Across every topic, the practical workflow is the same: define, formulate, solve, validate and communicate.
This guide follows that workflow, uses original examples rather than reproducing an assessment, and keeps the final-exam description deliberately limited to what the published source confirms.
Worked example · free
Formulate and solve a two-product capacity decision
- 1Let a and b denote non-negative quantities of products A and B. Maximise Z = 50a + 40b.
- 1Machine capacity gives 2a + b less than or equal to 100. Labour capacity gives a + 2b less than or equal to 80.
- 1Solving both boundaries gives a = 40 and b = 20. Both capacities are exactly used.
- 1The feasible axis corners are (50, 0), worth $2,500, and (0, 40), worth $1,600. The intersection is worth $2,800.
- 1Choose 40 units of A and 20 units of B for maximum contribution of $2,800, subject to the continuous-output assumption.
Key terms
- Decision variable
- A quantity the model is allowed to choose, defined with a unit, index and domain.
- Objective function
- The measurable performance criterion that the model maximises or minimises.
- Feasible solution
- A set of variable values satisfying every constraint and domain restriction.
- Binding constraint
- A constraint holding at equality at the reported solution, with zero slack.
- Slack
- Unused capacity in a less-than-or-equal resource constraint at a given solution.
- Shadow price
- The local change in optimal objective value from one more unit of a constraint right-hand side.
- Dual problem
- The optimisation problem that prices the constraints of the primal formulation.
- Flow conservation
- The rule that inflow plus supply equals outflow plus demand at a network node.
- Binary variable
- A variable restricted to zero or one for a yes-or-no decision or logical state.
- LP relaxation
- A version of an integer model with integrality removed, used to obtain a bound.
- Incumbent
- The best integer-feasible solution found so far during a discrete search.
- Optimality gap
- The difference between the incumbent value and the best remaining bound.
- Piecewise-linear function
- A relationship formed from connected linear segments with specified breakpoints.
- Convex optimisation
- Optimisation in which curvature and a convex feasible set can make a local minimum globally optimal.
ETF5248 FAQ
How is the unit assessed?
The Semester 2 materials list two individual assignments worth 15% each, a 20% individual mid-semester test and a 50% individual final examination. The two assignments are scheduled for Weeks 4 and 10. The four components sum to 100%, and the acquired sources do not state a hurdle for any component.
What is known about the final examination?
The published material confirms an individual final examination worth 50%, held in the final examination period and treated as a core-competency assessment. It does not state the duration, sections, question types or permitted materials. Use the official examination instructions when released rather than inferring the format from the mid-semester practice set.
How should I use the mid-semester practice set?
Use it to practise early-unit formulation and solution skills under time pressure, then diagnose each error by category: variable definition, coefficient, inequality direction, domain, calculation or interpretation. The practice document explicitly says it is not a mock test and is not indicative of test length, so do not treat its structure as an examination blueprint.
What do the assignments require?
Each assignment is an individual artefact worth 15%, and the unit pages provide separate R or Python submission routes. Assignment I is due in Week 4 on 21 August 2026, while Assignment II is due in Week 10 on 7 October 2026. Follow each published brief for task-specific deliverables and submission rules.
How do I choose the right optimisation model?
Start from the decision structure. Use continuous linear programming for divisible activity with linear relationships, network flow when movement occurs over nodes and arcs, integer programming for indivisible or logical choices, piecewise-linear models for changing marginal rates, and convex optimisation when genuine curvature satisfies the required global shape conditions.
What should I check after the solver returns an answer?
Recompute every left-hand side in original units, confirm domain and integrality, identify binding constraints and check the objective independently. For networks, reconcile every node and compare flow with a cut when relevant. For integer models, distinguish the incumbent from the bound and report the gap and solver tolerance.
What is the best final-review method?
Build one model-selection sheet that maps story cues to variables, objective, core constraint family and validation check. Then solve mixed problems from a blank page without copying a template. Finish each answer with the decision, objective value, resource or logical explanation, and one limitation of the model assumptions.
Questions students ask in each ETF5248 chapter
- What makes a model linear?
- Every objective and constraint expression must be a linear combination of variables with constant coefficients. Products of decision variables, powers, ratios with a variable denominator and logical either-or rules are not linear in their raw form. Constant setup data and fixed right-hand sides are allowed. Chapter 01 · Linear Programming Foundations
- Why is one inventory constraint not enough?
- Demand timing matters. A single total-production row can claim feasibility even when early demand occurs before enough production is available. One balance equation per period preserves chronology, and the closing value from one period becomes the opening value of the next. Chapter 02 · Business Models with Linear Programming
- Does a binding constraint always have a positive shadow price?
- No. Binding means the row has zero slack at the current solution, while the shadow price measures the local value of relaxing it. Degeneracy or redundancy can make a binding row worth zero. Report both facts rather than treating tightness and economic value as synonyms. Chapter 03 · Duality and Sensitivity Analysis
- How do I write node conservation?
- Choose one sign convention and keep it throughout. A useful form is outflow minus inflow equals supply, where supply is positive at an origin, zero at a transshipment node and negative at a demand node. Sum every incident directed arc exactly once with the correct sign. Chapter 04 · Network Flow Models
- Why not solve continuously and round?
- Independent rounding can violate capacity, coverage, assignment or logical constraints, and it can miss a better nearby integer combination. Integrality changes the feasible set itself. The integer model must be solved or a rounded proposal must be checked and compared through a valid discrete method. Chapter 05 · Integer Programming Decisions
- What is the difference between marginal and all-units pricing?
- Under marginal pricing, only quantity beyond a breakpoint receives the later rate, so segment costs add. Under an all-units tier, crossing a threshold changes the price applied to every unit. That discrete regime choice usually needs binary logic rather than simple continuous segment filling. Chapter 06 · Piecewise and Convex Optimisation
- What model-selection cues are most reliable?
- Use the underlying decision structure rather than one isolated word. Continuous divisible activity with constant rates is linear, arcs and conservation indicate networks, yes-or-no or count decisions require integers, changing marginal rates suggest piecewise segments, and smooth curvature requires a convexity check before claiming global optimality. Chapter 07 · Model Selection and Exam Review
How to study for the exam
Study ETF5248 as a sequence of modelling decisions, not as a list of solver commands. For each topic, take one business story and write five headings before doing any algebra: variables, objective, constraints, domains and interpretation. Put units beside every coefficient, because a unit mismatch often reveals an incorrect row before computation begins.
Solve small linear and network examples by hand so feasible regions, conservation and bounds remain visible. When software is used, keep an audit table containing each returned variable, every constraint left-hand side, slack, objective contribution and any solver status or gap. Rework the mid-semester practice questions, but respect the source warning that the set is not a mock and does not predict test length.
For final review, mix model families so the first task is classification rather than calculation. Practise explaining why a formulation is linear, why a binary link works in both states, why a shadow price is local, and why convexity is needed before a local answer becomes a global certificate. End every timed response with a plain-language recommendation and a check of feasibility, units and assumptions.
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