Multiple limiting factors

In this lesson

1. 0:00 Multiple limiting factors and linear programming
2. 0:39 Graphical linear programming fundamentals
3. 2:31 Five-step process for solving linear programming
4. 5:01 Defining variables and objective function
5. 8:03 Formulating constraints as inequalities
6. 11:18 Plotting constraints and identifying feasible region
7. 17:58 Testing corner points to find optimal solution
8. 25:57 Using ISO contribution line method
9. 31:58 Slack and shadow prices explained
10. 40:25 Solving simultaneous equations for corner points
11. 42:28 Practice question: materials and labour constraints
12. 45:47 Identifying binding constraints and slack

About this lesson

This is a core skill for Performance Management and Advanced Performance Management exams, where you'll encounter scenarios with constraints on labour, materials, and machine time simultaneously. You'll work through a complete five-step methodology: defining variables for the two products you're producing, establishing your objective function to maximise contribution, formulating all resource constraints as inequalities, constructing a graphical representation of the feasible region, and solving for the optimal production plan. The lesson walks you through a detailed worked example involving two products with five constraints, showing you how to plot each constraint, identify the feasible region, and test corner points to find the combination that generates maximum contribution. Beyond finding the optimal solution, you'll learn to identify binding and non-binding constraints, calculate slack (spare resources), and determine shadow prices. Shadow prices tell you the maximum premium you should pay to obtain additional units of a binding resource—essential knowledge for making realistic business decisions about overtime labour or sourcing extra materials. The lesson also covers solving simultaneous equations to find exact corner points where two constraints intersect, a technique you may need in the exam when reading values from graphs isn't sufficiently accurate. Throughout, you'll see how linear programming applies across real industries—construction, airlines, catering, and oil drilling—all facing multiple resource constraints. By the end, you'll be confident tackling multi-constraint optimisation questions and interpreting your results to support business decision-making.

Duration: 48m