Class 2: Profit Maximization and Risk Minimization as Dual Problems

Question 1

Why us Linear Programming?

Answer 1

Linear programs are easy (efficient) to solve

The best (optimal) solution is guaranteed to be found (if it exists)

Useful sensitivity analysis information is generated

Many problems are essentially linear: a large class of problems can be captured by linear programming

Question 2

What are some Business Applications for nonlinear programming?

Answer 2

Capital Budgeting
Portfolio Selection
Option Pricing
Production Planning
Inventory Management
Logistics and Transportation
Revenue Management
Product Mix
Many others

Question 3

Goals for Spreadsheet design?

Answer 3

Communication - A spreadsheet’s primary business purpose is communicating information to managers.

Reliability - The output a spreadsheet generates should be correct and consistent.

Auditability - A manager should be able to retrace the steps followed to generate the different outputs from the model in order to understand and verify results.

Modifiability - A well-designed spreadsheet should be easy to change or enhance in order to meet dynamic user requirements.

Question 4

what are the two concerns regarding portfolio selection

Answer 4

Question 5

What is the Pareto Optimization

Answer 5

When dealing with bi-objective problems:
Optimizing one objective
Threshold requirement for the other
objective

Portfolio Selection:
Maximizing the return while keeping an
upper limit for risk
Minimizing the risk while maintaining a
minimum return

Question 6

What are ways to lower risk?

Answer 6

Diversification results in lower risk. even if they are positively correlated

Lower correlation results in lower risk.
negatively correlated assets always yield lower risk than positively correlated pairs