You currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. The weights of these two portfolios are shown in the following table:

Stock A B C D E F G H Your Portfolio 0.12 0.15 0.13 0.10 0.20 0.10 0.12 0.08 M/V Portfolio 0.02 0.05 0.25 0.06 0.18 0.10 0.22 0.12

You would like to rebalance your portfolio in order to be closer to the M/V portfolio. To avoid excessively high transaction costs, you decide to rebalance only three stocks from your portfolio. Let xi denote the weight of stock i in your rebalanced portfolio. The objective is to minimize the quantity

|x1-0.02|+|x2-0.05|+|x3-0.25|+...+|x8-0.12|

which measures how closely the rebalanced portfolio matches the M/V portfolio.

Note that |.| denotes absolute value.

Formulate this problem as a mixed integer **linear** program