Formulation of Lp

The image you provided explains some key terms used in Linear Programming. Here's an easy-to-understand breakdown of the words and ideas:

1. Decision Variables

* What they are: These are the main choices you need to make in your problem.

* Easy explanation: Think of them as the "unknowns" you're trying to figure out. For example, if you own a bakery and want to maximize profit, your decision variables might be: "How many cakes should I bake?" and "How many cookies should I bake?" You don't know the exact numbers yet; that's what you're trying to find.

2. Objective Function

* What it is: This is a mathematical equation that represents your goal, whether it's maximizing profit or minimizing cost.

Easy explanation: It's the formula that tells you how your decision variables affect your main goal. For example, if each cake makes you $5 profit and each cookie makes you $2 profit, your objective function would be: Total Profit = 5 (Number of Cakes) + 2 * (Number of Cookies). The goal is to find the values for "Number of Cakes" and "Number of Cookies" that make this Total Profit as big as possible.

3. Coefficients in the Objective Function

* What they are: These are the numbers that are multiplied by the decision variables in the objective function.

* Easy explanation: These numbers tell you how much each decision variable contributes to your goal. In the bakery example, the "5" (for cakes) and the "2" (for cookies) are the coefficients. They are the "profit coefficients" because they show how much profit you get from baking one more cake or one more cookie.

4. Constraints

* What they are: These are the limitations or restrictions on your decision variables.

* Easy explanation: These are the rules you have to follow. For example, you might have a constraint like: "I only have 100 cups of flour." This sets a limit on how many cakes and cookies you can bake in total.

5. Coefficients in the Constraints

* What they are: These are the numbers that are multiplied by the decision variables within the constraint equations.

Easy explanation: These numbers tell you how much of a resource each decision variable uses up. For example, if a cake uses 2 cups of flour and a cookie uses 1 cup of flour, the constraint for your flour supply would look something like this: 2 (Number of Cakes) + 1 * (Number of Cookies) <= 100. The "2" and the "1" are the coefficients. They are called "input-output coefficients" because they show how much "input" (flour) is used for each unit of "output" (cake or cookie).

In a Nutshell:

You have a goal (the Objective Function) that you want to achieve by making certain choices (the Decision Variables). The numbers in your goal equation (the Objective Function Coefficients) show how much each choice helps you. But you're limited by a set of rules (the Constraints). The numbers in those rules (the Constraint Coefficients) tell you how much of a resource each choice uses up. The job of Linear Programming is to find the best values for your choices that make your goal as good as possible, without breaking any of the rules.