Linear Programming

Topics in this chapter

• Linear Programming Basics
• Problem Formulation
• Feasible Region Analysis
• Graphical Solution Method
• Corner-Point Optimization
• Special Solution Cases

Cheat sheet

Practice questions

1. Question 1Q-C583DE

   Which of the following points satisfies all the constraints x + y ≤ 6, x ≤ 4, y ≤ 5, x ≥ 0 and y ≥ 0?

   1. A.(4, 3)
   2. B.(2, 4)
   3. C.(5, 1)
   4. D.(1, 6)
   See the answer and solution
2. Question 2Q-8366FE

   Find the maximum value of Z = 3x + 2y subject to x + y ≤ 4, x ≤ 2, y ≤ 3, x ≥ 0 and y ≥ 0.

   1. A.6
   2. B.9
   3. C.10
   4. D.12
   See the answer and solution
3. Question 3Q-D26CE8

   For the linear programming problem: Maximise Z = x + y, subject to x + y ≥ 5, x ≥ 0 and y ≥ 0, which statement is correct?

   1. A.The problem has a unique maximum value.
   2. B.The feasible region is empty.
   3. C.The objective function has no finite maximum value.
   4. D.The maximum value is 5.
   See the answer and solution
4. Question 4Q-BBC65C

   A bakery produces cakes and pastries. Each cake requires 2 kg of flour and 1 hour of labour, while each pastry requires 1 kg of flour and 2 hours of labour. The bakery has 40 kg of flour and 30 labour hours available. It can sell at most 15 cakes and 20 pastries. The profit is Rs 60 per cake and Rs 50 per pastry. Formulate the corresponding linear programming problem.

   See the answer and solution
5. Question 5Q-47DE5B

   In a linear programming problem, a point that satisfies all the constraints, including the non-negativity restrictions, is called a:

   1. A.Feasible solution
   2. B.Optimal solution
   3. C.Infeasible solution
   4. D.Unbounded solution
   See the answer and solution