Why linear programming trips up so many South African students — and how to fix it
It's not really about the graphs. It's about turning a wordy real-world story into maths — all on your own.
Your child comes home with a maths problem about a factory that makes tables and chairs, or a farmer deciding how many hectares to plant with maize versus sunflowers. There are no obvious numbers to "solve for" — just a wordy paragraph, a handful of conditions, and an instruction to find the "maximum profit." They stare at it, unsure where to even start. If this scene feels familiar, your child has just met linear programming, and they are far from alone in finding it disorienting.
Linear programming appears in Grade 11 and returns, more demandingly, in Grade 12, as part of the CAPS Functions and Algebra strand. Parents often assume it should be manageable — after all, it's "just" straight-line graphs, something students have drawn since Grade 9. But it's rarely difficult because of the graphing. It's difficult because it asks students to build the maths themselves, from a real-world story, before they can even start solving.
Why linear programming feels like a different subject entirely
Most algebra topics hand students an equation and ask them to manipulate it. Linear programming does the opposite: it hands students a scenario — production limits, budget constraints, delivery capacities — and expects them to translate it into inequalities on their own. This is the step where most marks are lost, long before any graph gets drawn.
Consider a typical question: a company can spend at most a certain budget, has limited machine hours, and needs to work out how many units of two products to make for maximum profit. A student first defines variables, converts several sentences of English into a system of inequalities, graphs the feasible region, identifies the corner points, and finally tests those points in an objective function to find the optimal answer. That's five chained skills, and a slip at any single step — a wrong inequality sign, a mislabelled axis, a missed constraint — collapses the whole answer even if every calculation afterward is correct.
It also doesn't help that the vocabulary is easy to misread. Words like "at least," "at most," "no more than," and "exceeds" each point to a specific inequality sign, and mixing them up is one of the most common — and costly — mistakes in the topic.
Where South African students typically get stuck
- Turning words into inequalities. Many students can graph a given inequality perfectly but freeze when asked to write one from a description. This translation step is the real heart of the topic, and it's rarely practised in isolation.
- Mixing up "at least" and "at most." A single misread word flips an inequality sign the wrong way, shifting the entire feasible region and every answer that follows.
- Shading the wrong region. Even students who set up the correct inequality sometimes shade the region that satisfies the opposite condition, especially when several constraints overlap on one graph.
- Not testing all the corner points. The optimal solution always lies at a vertex of the feasible region — but students often guess, or test only the point that looks biggest, instead of substituting every vertex into the objective function.
- Losing marks on interpretation. Many papers ask students to explain what the answer means in context. Students who get the maths right still lose marks by not linking it back to the original scenario.
Why generic algebra practice doesn't fix it
Because linear programming borrows skills from earlier topics — solving inequalities, plotting straight lines, substitution — parents often assume reviewing "Grade 9 and 10 algebra" will patch the problem. It helps, but it's rarely enough alone. A student can be entirely comfortable graphing y = 2x + 3 and still have no idea how to turn "a farmer has no more than 60 hectares for two crops" into an inequality like x + y ≤ 60.
The maths isn't advanced. Building the model from a wordy scenario is the part nobody practises separately.
What actually helps is practice that isolates each stage: translating word problems into inequalities as its own drill, then graphing feasible regions separately, then working through objective functions and corner-point testing on their own, before combining all four into full past-paper questions. Equals2 tracks exactly where a student's answers go wrong — the setup, the graph, or the interpretation — and serves targeted practice on that specific weak link rather than generic algebra revision that may not touch the real gap.
What parents can do at home
You don't need to solve simultaneous inequalities yourself to help. A few habits make a genuine difference:
- Underline the constraint words first. "At least," "no more than," "cannot exceed" — have your child mark these before writing a single inequality. Slowing down here prevents the sign errors that quietly sink otherwise correct answers.
- Insist on a clearly labelled graph. Even for practice questions. Rushing the graph is where shading errors creep in, and a properly labelled feasible region makes it easier to sense-check an answer.
- Ask what the answer means, not just what it is. If your child can say "the factory should make 25 units of Product A to maximise profit," they've understood the topic. If they can only state a coordinate, the concept hasn't fully landed yet.
The bottom line
Linear programming isn't hard because the maths itself is advanced — most of it relies on skills your child has had since Grade 9 or 10. It's hard because it asks students to build the entire mathematical model themselves, and that translation step rarely gets dedicated practice. Break the process into its separate parts and drill the weakest one, and the topic becomes far more manageable than it first appears.
If your child is struggling with linear programming or any other Grade 11–12 topic, Equals2 pinpoints exactly which step is causing the trouble — across Grades 1 to 12 — and builds a practice plan around it.