1. Linear Optimization using Excel

2. 3-Steps Optimization Process
Model Development
Optimization
Evaluation
Model development is the most difficult part of the optimization process.
The evaluation involves sensitivity analysis of the optimized solution. It consists of the sensitivity analysis of the variables and the constraints.

3. Common Features Objective Input Variables Decision variables
Constraints
Objective to maximize or minimize
Input variables may be resources and profits
How many to make or allocate
Constraints might be machine hours, labour hours or demand.

4. Case 1
Saleem & Co manufactures jugs and glasses using machines A and B. The following hours are required to make one jug and glass: Machine A: 2 hours (for jug) and 1.5 hours (for glass) Machine B: 1.4 hours (for jug) and 1.1 hours (for glass) Total 400 hours are available on Machine A and 350 hours on Machine B. Contribution margin from jug is Rs. 15 and from glass Rs. 10. Required: Determine the optimal mix of jugs and glasses in order to maximize the contribution

5. Case 2
Pak-Suzuki makes two types of air-filters: regular and premium. The unit profit of each of them is Rs. 500 and Rs Both uses the following inputs: Labour Hours: 3 (Reg.) and 4 (Prem.) ---- Max. Cap hrs Plastic components: 2 (Reg.) and 3 (Prem.) --- Max. Cap comp. Machine hours: 0.75 (Reg.) and 1.20 (Prem.) --- Max. Cap hrs Required: Optimal product mix of the regular and the premium air filters

6. Case 3
Pak-Suzuki makes two types of air-filters: regular and premium. The unit profit of each of them is Rs. 500 and Rs Both uses the following inputs: Labour Hours: 3 (Reg.) and 4 (Prem.) ---- Max. Cap hrs Plastic components: 2 (Reg.) and 3 (Prem.) --- Max. Cap comp. Machine hours: 0.75 (Reg.) and 1.20 (Prem.) --- Max. Cap hrs Demand: Max. (Reg.) 500 and Max. (Prem.) 400 Required: Optimal product mix of the regular and the premium air filters

7. Case 4
Required: Use the following information to find the optimal product mix of mice, keyboards and USB hubs.

8. Case 5 Investment Optimization
Ali wants to invest Rs. 1,000,000/- in the financial assets in Pakistan. His analysis shows the following expected profits on the major asset classes:
Derivatives 28% High Risk
Equity 21% High Risk
Bonds 16% Low Risk
Money Market 13% Low Risk
He does not want to invest more than 35% in anyone of the asset classes and more than 60% in the high risk assets.
Required: Optimal portfolio mix that maximizes the annual return.