📚 Topic Summary
Linear programming is a method to achieve the best outcome (like maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. These relationships are inequalities or equalities. We seek to optimize an objective function subject to constraints. Printable practice problems help solidify understanding and build problem-solving skills.
The goal of linear programming is to find the optimal solution to a problem that can be modeled with linear equations. This often involves graphing inequalities to find a feasible region and then testing the vertices of that region to find the maximum or minimum value of an objective function.
🧠 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Objective Function |
a. A condition that must be satisfied. |
| 2. Constraint |
b. The set of all possible solutions that satisfy all constraints. |
| 3. Feasible Region |
c. A function to be maximized or minimized. |
| 4. Optimal Solution |
d. The point within the feasible region that yields the best value of the objective function. |
| 5. Decision Variables |
e. Variables that represent the quantities to be determined. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct words:
In linear programming, the goal is to find the _______ solution that either _______ or _______ the objective function, subject to a set of _______. The region that satisfies all constraints is called the _______ _______.
🤔 Part C: Critical Thinking
Explain, in your own words, how linear programming can be used in a real-world business scenario. Provide a specific example.