SCCUR 98 California State Polytechnic University, Pomona SCE/EIC.
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![Page 1: Operations Research I IE 416 California State Polytechnic University, Pomona Operations Research I IE 416 California State Polytechnic University, Pomona.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649edb5503460f94bebe5d/html5/thumbnails/1.jpg)
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 StatementSummary of problemFormulation of problemWinQSB Inputs and OutputsSolution Summary Objective Function Sensitivity AnalysisRHS Sensitivity AnalysisReport to Manger
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Problem Statement
![Page 4: Operations Research I IE 416 California State Polytechnic University, Pomona Operations Research I IE 416 California State Polytechnic University, Pomona.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649edb5503460f94bebe5d/html5/thumbnails/4.jpg)
Summary of the ProblemParisay: needs modification based on my notes in Word file.
X1
X2
X21
X31
X32
X4
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Formulation of Problem
Variables:X1 = Number of ounces of Product 1 soldX2 = Number of ounces of Product 2 soldX21 = Number of ounces of Product 2 sold after producing Product 1X31 = Number of ounces of Product 3 sold after producing Product 1X32 = Number of ounces of Product 3 sold after producing Product 2X4 = Number of pounds of raw materials
Objective Function: OF: Z= Profit =Total Revenue – processing costs – purchase cost
Maximize Z = 10X1 + 20X2 + 20X21 + 30X31 + 30X32 – 26X4 –1X21 – 2X31 – 6X32
Practical Conversion:1lb = 16oz.
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Constraints:Maximum amount of Product 1 that can be sold (ounces): X1 ≤ 5000Maximum amount of Product 2 that can be sold (ounces): X2 + X21 ≤ 5000Maximum 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 ≥ 0X21 ≥ 0 X31 ≥ 0X32 ≥ 0 X4 ≥ 0
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WinQSB Input
![Page 8: Operations Research I IE 416 California State Polytechnic University, Pomona Operations Research I IE 416 California State Polytechnic University, Pomona.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649edb5503460f94bebe5d/html5/thumbnails/8.jpg)
WinQSB Output
![Page 9: Operations Research I IE 416 California State Polytechnic University, Pomona Operations Research I IE 416 California State Polytechnic University, Pomona.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649edb5503460f94bebe5d/html5/thumbnails/9.jpg)
Solution Summary
# lb of Raw Materials 3,250 lb
# ounces product 1 sold 5,000 oz.
# ounces product 2 sold 3,250 oz.
# ounces product 1 product 2 1,750 oz.
# ounces product 1 product 3 3,000 oz.
# ounces product 2 product 3 None
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.
![Page 13: Operations Research I IE 416 California State Polytechnic University, Pomona Operations Research I IE 416 California State Polytechnic University, Pomona.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649edb5503460f94bebe5d/html5/thumbnails/13.jpg)
Sensitivity Analysis of RHS
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Sensitivity Analysis of RHS
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Sensitivity Analysis of RHS
Total profit changes from $147,750 to $191,250 which is a $43,500 gain.
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Report to ManagerParisay: it is better to add unit to the last column
•Maximum Profit: $147,750.00
Variable Quantity Net Loss/Profit
# lb of Raw Materials 3,250 lb Cost: $26/lb
# ounces product 1 sold 5,000 oz. Profit: $10/oz
# ounces product 2 sold 3,250 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 ?