4. Operations Analytics

Linear Programming — Quiz

Test your understanding of linear programming with 5 practice questions.

Practice Questions

Question 1

Which of the following equations correctly models the assembly time constraint for two products A and B if each unit of A requires 3 hours, each unit of B requires 2 hours, and a maximum of 180 hours of assembly time are available?

Question 2

In the constraint $4x + y + s = 100$, if at a feasible solution the slack variable $s$ equals 20, what does this indicate about resource utilization?

Question 3

Solve the LP: Maximize $Z = 7x + 4y$ subject to $2x + 3y \le 12$, $x + y \le 5$, $x, y \ge 0$. What is the optimal solution and optimal value of $Z$?

Question 4

In the simplex method for a maximization problem, a non-basic variable has a reduced cost $(c_j - z_j)$ of 5. What does this imply?

Question 5

During the simplex method, if all reduced costs $(c_j - z_j)$ for non-basic variables are non-positive, what condition has been met?