Operations Research I IE 416 California State Polytechnic University, Pomona Operations Research I...
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Transcript of Operations Research I IE 416 California State Polytechnic University, Pomona Operations Research I...
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
Outline
Problem StatementSummary of problemFormulation of problemWinQSB Inputs and OutputsSolution Summary Objective Function Sensitivity AnalysisRHS Sensitivity AnalysisReport to Manger
Problem Statement
Summary of the ProblemParisay: needs modification based on my notes in Word file.
X1
X2
X21
X31
X32
X4
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.
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
WinQSB Input
WinQSB Output
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
Sensitivity Analysis of O.F.Parisay: refer to my comments in Word file
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.
Sensitivity Analysis of O.F.
Sensitivity Analysis of RHS
Sensitivity Analysis of RHS
Sensitivity Analysis of RHS
Total profit changes from $147,750 to $191,250 which is a $43,500 gain.
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 -
Questions ?