MATHS PRACTICAL//LAB 42//LINEAR PROGRAMMING PROBLEM//HOW TO WRITE IN OBSERVATION BOOK

Introduction

This tutorial focuses on how to effectively document a linear programming problem in an observation book as demonstrated in the YouTube video by Albin Kattakada. Understanding how to write observations is crucial for students conducting mathematical experiments, as it ensures clarity and precision in recording results.

Step 1: Prepare Your Observation Book

• Choose a clean and organized observation book.
• Write your name, roll number, and date on the first page.
• Create a table of contents for easy navigation.

Step 2: Title Your Experiment

• Clearly label the title of the experiment at the top of the page.
• Use a descriptive title, such as "Linear Programming Problem Analysis."

Step 3: State the Objective

• Begin with a clear statement of the objective of the experiment.
• Example: "To solve a linear programming problem graphically."

Step 4: Gather Required Data

• List all the variables involved in the problem.
• Write down the constraints and the objective function.
• Example of a linear programming objective function:

  Maximize Z = 3x + 4y
  

• Include the constraints:

  Subject to:
  x + 2y ≤ 8
  3x + y ≤ 12
  x ≥ 0, y ≥ 0
  

Step 5: Graph the Constraints

• Draw the graph for the constraints listed.
• Label the axes appropriately (e.g., x-axis and y-axis).
• Plot the lines for each constraint on the graph.
• Identify the feasible region where all constraints overlap.

Step 6: Identify Corner Points

• Determine the corner points of the feasible region.
• Calculate the coordinates of each corner point by solving the equations of the lines where they intersect.

Step 7: Evaluate the Objective Function

• Substitute the coordinates of each corner point into the objective function.
• Calculate the values of Z for each point.

Step 8: Determine the Optimal Solution

• Identify the corner point that gives the maximum value of Z.
• Clearly state the optimal solution in your observation book.
• Example: "The optimal solution occurs at (x, y) = (2, 3) with a maximum Z = 18."

Step 9: Conclusion

• Summarize the findings from your experiment.
• Reflect on any challenges faced and how they were overcome.
• Include any additional insights or real-world applications of linear programming.

Conclusion

This tutorial has outlined the necessary steps for documenting a linear programming problem in your observation book. By following these steps, you can ensure that your experiments are well-organized and clearly presented. For further practice, consider exploring additional problems or reviewing the accompanying PDF for Lab 42 answers.