7. Linear Programming

Try these first

1. 1.

   What is the objective function in a linear programming problem?

   Hint

   Think about what we are trying to achieve in the problem.

2. 2.

   What are constraints in linear programming?

   Hint

   Consider the limits placed on resources in a problem.

3. 3.

   What is the primary goal of linear programming?

   • To solve equations
   • To maximize or minimize a function
   • To calculate averages

   Hint

   Think about optimization.

4. 4.

   True or False: The feasible region in linear programming can never be empty.

   • True
   • False

   Hint

   Recall situations where constraints might conflict.

5. 5.

   Design a linear programming model for a factory producing two types of toys with varying profit margins and material constraints. Identify the feasible region graphically.

   Hint

   Dive into the limitation and profit margin for each toy.

6. 6.

   Using the graphical method, resolve the following linear programming problem: Maximize Z = 3x + 4y, subject to x + 2y ≤ 8 and 3x + y ≤ 8.

   Hint

   The intersection of constraints will help you find the vertex points.