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Operations Research I IE 416 California State Polytechnic University, Pomona

Operations Research I IE 416 California State Polytechnic University, Pomona. Linear programming Homework #4 on Page 97. TEAM 5 Serina Alkejek Harmeet Hora Kaveh “Kevin” Shamuilian. Problem Statement Summary of problem Formulation of problem WinQSB Inputs and Outputs

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Operations Research I IE 416 California State Polytechnic University, Pomona

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  1. Operations Research I IE 416California State Polytechnic University, Pomona Linear programming Homework #4 on Page 97 TEAM 5 SerinaAlkejek HarmeetHora Kaveh “Kevin” Shamuilian

  2. Problem Statement • Summary of problem • Formulation of problem • WinQSB Inputs and Outputs • Solution Summary • Objective Function Sensitivity Analysis • RHS Sensitivity Analysis • Report to Manger Outline

  3. Problem Statement

  4. X1 X21 X4 X31 X2 Summary of the ProblemParisay: needs modification based on my notes in Word file. X32

  5. Practical Conversion: 1lb = 16oz. Variables: X1 = Number of ounces of Product 1 sold X2 = Number of ounces of Product 2 sold X21 = Number of ounces of Product 2 sold after producing Product 1 X31= Number of ounces of Product 3 sold after producing Product 1 X32= Number of ounces of Product 3 sold after producing Product 2 X4 = Number of pounds of raw materials Objective Function: OF: Z= Profit =Total Revenue – processing costs – purchase cost MaximizeZ = 10X1 + 20X2 + 20X21 + 30X31 + 30X32 – 26X4 –1X21– 2X31 – 6X32 Formulation of Problem

  6. Constraints: Maximum amount of Product 1 that can be sold (ounces): X1 ≤ 5000 Maximum amount of Product 2 that can be sold (ounces): X2 + X21 ≤ 5000 Maximum amount of Product 3 that can be sold (ounces): X31 + X32 ≤ 3000 Amt. of Product 1 available after raw material processing (ounces): 3X4= X1 + X21 + X31 Amount of Product 2 available after raw material processing (ounces): X4= X2 + X32 Maximum labor hours available (hours): 2X4+ 2X21 + 3X31 + 1X32 ≤ 25000 Formulation Of Problem Sign Constraint: X1 ≥ 0 X2≥ 0 X21 ≥ 0 X31≥ 0 X32 ≥ 0 X4≥ 0

  7. WinQSB Input

  8. WinQSB Output

  9. Solution Summary Maximum profit : $147,750.00

  10. Sensitivity Analysis of O.F.Parisay: refer to my comments in Word file

  11. If the “#oz prod 2 sold after producing 1” increases from 19 to 24 • maximum profit will increase to $156,500.00, a favorable difference of $8,750. Sensitivity Analysis of O.F.Parisay: use graph not table

  12. Sensitivity Analysis of O.F.

  13. Sensitivity Analysis of RHS

  14. Sensitivity Analysis of RHS

  15. Sensitivity Analysis of RHS • Total profit changes from $147,750 to $191,250 which is a $43,500 gain.

  16. Maximum Profit: $147,750.00 Report to ManagerParisay: it is better to add unit to the last column

  17. Questions ?

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