1. 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

2. 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

3. Problem Statement

4. Summary of the Problem Parisay: needs modification based on my notes in Word file. X1X1 X2X2 X 21 X 31 X 32 X4X4

5. 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.

6. 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

7. WinQSB Input

8. WinQSB Output

9. 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

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

11. 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.

12. Sensitivity Analysis of O.F.

13. Sensitivity Analysis of RHS

15. Total profit changes from $147,750 to $191,250 which is a $43,500 gain.

16. 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-

17. Questions ?