7.1. Introduction to Linear Programming

Try these first

1. 1.

   Define linear programming.

   Hint

   What does 'linear' refer to in this context?

2. 2.

   What is an objective function?

   Hint

   It represents the goal of our optimization problem.

3. 3.

   What is the primary goal of linear programming?

   • To create complex functions
   • To maximize or minimize a linear function
   • To generate random numbers

   Hint

   Remember what 'linear programming' involves in its name.

4. 4.

   True or False: The feasible region can be empty if constraints are too strict.

   • True
   • False

   Hint

   Consider the implications of constraints on solutions.

5. 5.

   A factory produces three products: A, B, and C. Product A nets $500, B nets$300, and C nets $400. There are producing limits due to material constraints. Formulate a linear programming model to maximize profits.

   Hint

   Follow the step-by-step formulation discussed in class.

6. 6.

   Given constraints A + 2B ≤ 20, 3C + 2A ≤ 30, and A, B, C ≥ 0, graph the inequalities and find the feasible region.

   Hint

   Use graphing techniques and understand how inequalities create boundaries.