Homework

1. Chapter 8: #3 (Note, there are no constraints for this problem)

2. Chapter 8: #9

3. Chapter 8: #21

4. Alex has money to invest in some combination of four investments (I1, I2, I3, and I4). There are three scenarios (A, B, and C) that may occur, and each investment will give a different return under each scenario (see below table, where the numbers indicate the percent return under each scenario). The probability of scenario A is 0.35, the probability of scenario B is 0.25, and the probability of scenario C is 0.4.

a) Formulate and solve the Markowitzian mean-variance problem of determining the portfolio which minimizes variance while maintaining an expected return of at least 2.5%.

b) Formulate and solve the Markowitzian mean-variance problem of determining the portfolio which maximizes expected return while maintaining a variance of no more than 30.

5. Three cleaning crews are available for a job that requires an area of 1000 square feet to be cleaned. Each cleaning crew charges a fixed cost that is only charged if the company is hired and a variable cost that is dependent on the number of square feet cleaned (see below). The job can be performed either by a single cleaner or by a combination of cleaners. Formulate and solve a mathematical programming model that will determine which crews to hire and how much (in square feet) of the job that each should do.

Company A Cost = 0.01x2 - 2x + 2000

Company B Cost = 0.005x2 + x + 4000

Company C Cost = 0.01x2 - x + 1000