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QM B Lego Simplex

QM B Lego Simplex. Scenario. You manufacture tables and chairs. Tables and chairs are manufactured from small and large bricks. Small brick. Large brick. Lego Simplex Data. Table 2 large bricks 2 small bricks $16 profit. Chair 1 large bricks 2 small bricks $10 profit.

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QM B Lego Simplex

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  1. QM B Lego Simplex

  2. Scenario • You manufacture tables and chairs. • Tables and chairs are manufactured from small and large bricks. Small brick Large brick

  3. Lego Simplex Data • Table • 2 large bricks • 2 small bricks • $16 profit • Chair • 1 large bricks • 2 small bricks • $10 profit

  4. Lego My Simplex Resources • You have 8 small bricks and 6 large bricks

  5. The Goal • How many tables and how many chairs should be produced to maximize profit? Buzz Group Question 1 Groups of 3-4

  6. One possible solution Is this solution optimal? Profit = 3*16 = $48 Give up a table (-$16) Make two chairs (+20) Improves the solution by $4. So the above solutions is not optimal.

  7. Optimal Solution 2 tables 2 chairs Profit: $52

  8. Formulate as an LP Buzz Group: Question 2 Be sure to: Define variables Write the objective function Write the constraints Include non-negativity constraints

  9. Formulate as an LP T – number of tables to produce C – number of chairs to produce Max 16 T + 10 C Subject to: 2 T + C  6 Large bricks 2 T + 2 C  8 Small bricks T  0, C  0 Non-negativity

  10. Graphical Insight 2 T + C  6 2 T + 2 C  8

  11. At the optimal solution: • What if one more large brick becomes available? Buzz Group: Question 3

  12. What would you be willing to pay for the brick? • Take a chair apart: (-10) • Pay a maximum of $6. This is the shadow price for large bricks – the increase in the objective function if one more unit of the resource, large bricks, becomes available. • Make a table: (+16)

  13. How many large bricks should you buy at $6? • If we have yet another additional large bricks (8 altogether), then we can take apart the second chair and make a table. ($6 improvement). • If we add one more large brick (9 altogether), can we make another table?

  14. Allowable increase • The number of additional large bricks that are worth the shadow price of $6 is 2.

  15. Sensitivity Analysis • Shadow Prices – increase in the objective function if one more unit of the resource becomes available • Allowable increases • amount that the resource can increase and have the shadow price stay the same; • if outside the allowable increase, change RHS and re-run.

  16. Sensitivity Report

  17. Think-pair-share: Stratton – Sensitivity Analysis • What is the optimal product mix? • What is the unused capacity of each resource? • An additional labor hour is available. Where should that labor hour be assigned? • An additional 8 labor hours are available. Where should these labor hours be assigned? • The material manager has found an additional 2 pounds of additive mix for $1.20 per pound. Should he procure this additional mix?

  18. Stratton Sensitivity Analysis • What is the optimal product mix 3 packages of Pipe 1 6 packages of Pipe 2 • What is the unused capacity of each resource: Extrusion hours: 0 hours Packaging hours: 0 hours Additive mix: 4 pounds

  19. Stratton Sensitivity Analysis • An additional labor hour is available, where should that labor hour be assigned? Packaging – for every additional hour of packaging, profit increases $11 (up to a 2 hours increase)

  20. Stratton Sensitivity Analysis • An additional 8 labor hours are available. Where should these labor hours be assigned? Need to re-run the model since 8 hours is larger than the allowable increase for both labor hour constraints.

  21. Stratton Sensitivity Analysis • The material manager has found an additional 2 pounds of additive mix for $1.20 per pound. Should he procure this additional mix? No, the current optimal solution does not use all of the additive mix that is available.

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