The brokerage firm Michel Awski Ltd. is proposing investment guidelines for its middle-income investors. Currently, they are considering investments in several areas. Only whole units (integer) of an investment can be purchased.

To: From:	Hamilton Regina
Kingston Prince George	$30 $40 $45 $66
Sudbury Abbotsford	$38 $27 $30 $50

Investment type	Cost per unit ($)	Expected annual return per unit ($)
large cap common stock	1200	60
small cap common stock	3100	186
preferred stock	7000	385
government bonds	4500	292
industrial bonds	6000	312
hi-tech mutual funds	3800	220
energy mutual funds	2800	154

Mr. and Mrs. Kaushon would like to invest $25,000. In addition to maximizing expected annual return, several additional restrictions on the investment portfolio have been agreed upon, with to deal with diversity of portfolio and risk considerations. These restrictions are:

• at most one of the two common stock investments types should be made;

• either both or neither of large cap common stock and preferred stock should appear in the

  portfolio;

• hi-tech mutual funds will not be in the portfolio unless preferred stock is also in the portfolio;

• energy mutual funds will not be in the portfolio unless both government bonds and industrial

  bonds are in the portfolio.

1. Formulate the Integer/Binary Linear Programming model in algebraic form. Define the decision variables, objective function, and constraints.