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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
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Outline Problem Statement Summary of problem Formulation of problem WinQSB Inputs and Outputs Solution Summary Objective Function Sensitivity Analysis RHS Sensitivity Analysis Report to Manger
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Problem Statement
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Summary of the Problem Parisay: needs modification based on my notes in Word file. X1X1 X2X2 X 21 X 31 X 32 X4X4
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Formulation of Problem Variables: X 1 = Number of ounces of Product 1 sold X 2 = Number of ounces of Product 2 sold X 21 = Number of ounces of Product 2 sold after producing Product 1 X 31 = Number of ounces of Product 3 sold after producing Product 1 X 32 = Number of ounces of Product 3 sold after producing Product 2 X 4 = Number of pounds of raw materials Objective Function: OF: OF: Z= Profit =Total Revenue – processing costs – purchase cost Maximize Z = 10X 1 + 20X 2 + 20X 21 + 30X 31 + 30X 32 – 26X 4 –1X 21 – 2X 31 – 6X 32 Practical Conversion: 1lb = 16oz.
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Constraints: Maximum amount of Product 1 that can be sold (ounces): X 1 ≤ 5000 Maximum amount of Product 2 that can be sold (ounces): X 2 + X 21 ≤ 5000 Maximum amount of Product 3 that can be sold (ounces): X 31 + X 32 ≤ 3000 Amt. of Product 1 available after raw material processing (ounces): 3X 4 = X 1 + X 21 + X 31 Amount of Product 2 available after raw material processing (ounces): X 4 = X 2 + X 32 Maximum labor hours available (hours): 2X 4 + 2X 21 + 3X 31 + 1X 32 ≤ 25000 Formulation Of Problem Sign Constraint: X 1 ≥ 0 X 2 ≥ 0 X 21 ≥ 0 X 31 ≥ 0 X 32 ≥ 0 X 4 ≥ 0
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WinQSB Input
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WinQSB Output
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Solution Summary # lb of Raw Materials 3,250 lb # ounces product 1 sold5,000 oz. # ounces product 2 sold3,250 oz. # ounces product 1 product 21,750 oz. # ounces product 1 product 33,000 oz. # ounces product 2 product 3None Maximum profit : $147,750.00
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Sensitivity Analysis of O.F. Parisay: refer to my comments in Word file
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Sensitivity Analysis of O.F. Parisay: use graph not table 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.
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Sensitivity Analysis of O.F.
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Sensitivity Analysis of RHS
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Total profit changes from $147,750 to $191,250 which is a $43,500 gain.
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Report to Manager Parisay: it is better to add unit to the last column Maximum Profit: $147,750.00 VariableQuantityNet Loss/Profit # lb of Raw Materials 3,250 lbCost: $26/lb # ounces product 1 sold5,000 oz.Profit: $10/oz # ounces product 2 sold3,250 oz.Profit: $20 # ounces product 1 product 2 1,750 oz.Profit: $19 # ounces product 1 product 3 3,000 oz.Profit:$28 # ounces product 2 product 3 None-
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Questions ?
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