Sensitivity analysis Example

Duration: 11 min

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AI Summary

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This video presents a step-by-step solution to a linear programming problem, using a furniture manufacturing scenario. The instructor begins by introducing the problem, which involves a manufacturer producing desks, tables, and chairs. He then systematically defines the decision variables, formulates the objective function to maximize profit, and identifies the constraints based on limited resources: timber, finishing time, and carpentry time. The constraints are derived from the resource requirements per unit of each product and the total available weekly resources. The final model is presented as a standard linear programming problem: maximize profit subject to the resource constraints and non-negativity conditions. The video concludes with the complete mathematical formulation on the whiteboard.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a man standing in front of a whiteboard titled 'Linear Programming Problem'. He begins to set up a word problem, writing 'A manufacturer of furniture makes' and then listing the products: 'desks, tables, chairs'. He also writes 'Function' and 'Maximise' to indicate the goal of the problem, which is to maximize profit from the production of these items.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to build the problem by detailing the resource requirements for each product. He writes that to make a desk, 8 ft of timber, 4 hours of finishing time, and 2 hours of carpentry time are needed. For a chair, the requirements are 6 ft of timber, 2 hours of finishing, and 1.5 hours of carpentry. For a table, it's 1 ft of timber, 1.5 hours of finishing, and 0.5 hours of carpentry. He then writes 'Resource' to label this section.

  3. 5:00 – 10:00 05:00-10:00

    The instructor specifies the total available weekly resources: 48 ft of timber, 20 hours of finishing time, and 8 hours of carpentry time. He then states the unit profit for each item: $60 for a desk, $30 for a chair, and $20 for a table. He writes 'Objective' and begins to formulate the objective function, which is to maximize profit.

  4. 10:00 – 11:17 10:00-11:17

    The instructor defines the decision variables: let x1, x2, x3 be the number of desks, chairs, and tables to be produced, respectively. He then writes the complete linear programming model: Maximize Z = 60x1 + 30x2 + 20x3, subject to the constraints 8x1 + 6x2 + x3 ≤ 48 (timber), 4x1 + 2x2 + 1.5x3 ≤ 20 (finishing), and 2x1 + 1.5x2 + 0.5x3 ≤ 8 (carpentry), with x1, x2, x3 ≥ 0. He boxes the final model on the board.

The video provides a clear, structured walkthrough of formulating a linear programming problem from a real-world scenario. It demonstrates the essential steps: identifying the decision variables, defining the objective function (maximizing profit), and establishing the constraints based on limited resources. The progression from a narrative problem to a precise mathematical model is logical and pedagogical, making it an effective example for students learning to model optimization problems.