5. Decision Mathematics

Linear Programming — Quiz

Test your understanding of linear programming with 5 practice questions.

Practice Questions

Question 1

A company manufactures two products, Product X and Product Y. Each unit of Product X requires 2 hours on Machine A and 1 hour on Machine B. Each unit of Product Y requires 1 hour on Machine A and 3 hours on Machine B. Machine A is available for a maximum of 100 hours, and Machine B is available for a maximum of 120 hours. If $x$ represents the number of units of Product X and $y$ represents the number of units of Product Y, which of the following systems of inequalities correctly represents the constraints for machine availability?

Question 2

When using the graphical method to solve a linear programming problem, what is the primary reason for evaluating the objective function at the vertices of the feasible region?

Question 3

Consider a linear programming problem with the objective function to maximize $P = 5x + 2y$ subject to the constraints: $x \ge 0$, $y \ge 0$, $x + y \le 6$, and $x \le 4$. Which of the following points is a vertex of the feasible region that could yield the optimal solution?

Question 4

In the context of the Simplex method, what is the role of a pivot element?

Question 5

A linear programming problem is formulated to minimize costs. The primal problem has a feasible solution. Which of the following statements about its dual problem is always true?