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 ?