A linear programme optimises a linear objective over a polyhedron, so if an optimum exists it is attained at a vertex — and the dual programme tells you whether one exists at all.
Linear Programming
Feasible regions, the simplex method and duality — the part of Unit 4 that is not statistics, and the one most often left out of a preparation plan.
3 previous-year questions from this topic → every option and the correct answer, free · where the marks are
1. Linear programming, simplex and duality
Exam focus: Part C sets these as multi-statement questions about a single programme: whether it is feasible, whether the optimum is attained, whether it is unbounded, and what the dual says. The arithmetic is light; the marks turn on reading the constraints exactly.
Part C2024 Decembershow ▾Consider maximizing the objective function subject to . Then, which of the following statements are true?
- A.The optimal solution is 4.
- B.An optimal point is (4, 1, 0).
- C.The optimal solution is 6.
- D.(1/2, 0, 0) is a corner point.✓
The worked solution and the per-option analysis are in Trap Analysis.
Part C2024 Decembershow ▾Consider maximizing the objective function subject to . Then, which of the following statements are true?
- A.(5, 0, 1) is a corner point.✓
- B.(4, 1, 1) is an optimal point.
- C.The optimal solution is 9.
- D.The optimal solution is 10.✓
The worked solution and the per-option analysis are in Trap Analysis.
Part C2024 Juneshow ▾Consider the linear programming problem: max{} subject to constraints , and . Which of the following statements are true?
- A.The optimum value is 3✓
- B.The optimum value is 3/2
- C.(0, 2, 1) is an extreme point of the feasible region✓
- D.(1/2, 0, 1) is the optimal solution
The worked solution and the per-option analysis are in Trap Analysis.