7.5. Simplex Algorithm Overview

Try these first

1. 1.

   Define linear programming in your words.

   Hint

   Think about the context of maximizing profits or minimizing costs.

2. 2.

   What happens at the vertices of the feasible region?

   Hint

   Consider how the simplex algorithm operates.

3. 3.

   What is the main purpose of the simplex algorithm?

   • To maximize profit
   • To minimize constraints
   • To optimize linear functions

   Hint

   Revisit the definition of the simplex algorithm.

4. 4.

   True or False: A feasible region can be unbounded.

   • True
   • False

   Hint

   Think about what happens when constraints allow for infinite possibilities.

5. 5.

   Consider a factory producing two products. Product A requires 2 hours of labor per unit, and Product B requires 3 hours. There are 100 hours available. Product A gives a profit of $4 per unit, while Product B gives$5. Formulate a linear programming problem.

   Hint

   Identify variables and state the relationships using inequalities.

6. 6.

   Create a scenario where multiple constraints affect profit maximization in a linear programming problem with the potential for unbounded solutions.

   Hint

   Think of variables that may affect delivery while considering a budget.