Linear Programming in MYP Extended Maths
Learn linear programming in MYP Extended Maths Year 5. Master objective functions, constraints, feasible regions and optimisation for Criterion D application tasks.
What Is Linear Programming?
Linear programming is a mathematical method for finding the best outcome — maximum profit, minimum cost, optimal allocation — subject to a set of linear constraints. It sits at the intersection of algebra, graphing, and real-world decision making, making it ideal for Criterion D application tasks at Extended level.
Core Components
Decision Variables
Define the quantities you are optimising. For example, let x = number of product A and y = number of product B produced per day. Every other expression in the problem is written in terms of these variables.
Constraints
Constraints are linear inequalities that represent real limitations — time, materials, capacity, minimum requirements. For example: 2x + 3y ≤ 120 (material limit), x ≥ 0, y ≥ 0 (non-negativity). Each constraint is graphed as a boundary line, and the feasible region is the set of all points that satisfy every constraint simultaneously.
The Feasible Region
The feasible region is typically a polygon on the graph, bounded by the constraint lines. Every point inside (or on the boundary of) this region is a valid solution. You identify the feasible region by shading — some teachers shade the unwanted region, others shade the feasible region. Be consistent and label clearly.
The Objective Function
The objective function is the expression you want to maximise or minimise — for example, P = 5x + 8y (profit). The optimal solution always occurs at a vertex (corner point) of the feasible region. Evaluate the objective function at each vertex and select the maximum or minimum value.
Common Mistakes
- Shading the wrong side of a constraint line — substitute a test point (usually the origin) to check.
- Forgetting to include non-negativity constraints (x ≥ 0, y ≥ 0).
- Evaluating the objective function at non-vertex points — the optimum is always at a corner.
- Not stating the final answer in context — state the values of both variables and the optimal objective value.
Criterion D Connection
Linear programming problems are natural Criterion D tasks. You will be expected to define variables, set up constraints from a verbal description, identify the feasible region, and interpret the optimal solution in the real-world context. Writing a clear conclusion — not just a number — is essential.