LPP of how many variables can be solved by graphical method?

Options

A. Three variables
B. Two variables
C. More than three variables
D. None of the above

Answer

To determine how many variables can be solved by the graphical method in Linear Programming Problems (LPP), we can follow these steps:

### Step 1: Understand the Graphical Method
The graphical method is a way to solve LPPs by plotting the constraints on a graph. Each constraint is represented as a line in a two-dimensional space (2D), where the x-axis and y-axis represent the variables.

**Hint:** Remember that the graphical method is limited to visualizing problems in a 2D space.

### Step 2: Identify the Number of Variables
In LPP, we typically deal with two variables, commonly denoted as x and y. This is because we can plot these two variables on a two-dimensional graph.

**Hint:** Think about how many dimensions you can represent on a standard graph.

### Step 3: Analyze the Constraints
For example, consider the constraints:
1. \( x + 2y \leq 5 \)
2. \( x + 3y \leq 1 \)

These inequalities can be graphed, and the feasible region (the area that satisfies all constraints) can be identified.

**Hint:** Each inequality will create a line on the graph, and the area that satisfies all inequalities will be your feasible region.

### Step 4: Limitations of the Graphical Method
If we have more than two variables (e.g., three variables x, y, and z), we cannot represent them in a two-dimensional graph. Instead, we would need to use three-dimensional space, which is much more complex and not typically done graphically.

**Hint:** Consider how many axes you need to represent additional variables.

### Step 5: Conclusion
Thus, the maximum number of variables that can be effectively solved using the graphical method in LPP is **two**.

**Final Answer:** The graphical method can solve LPPs with a maximum of **2 variables**.