# 115finalF06s - ENGRI 115, Fall 2006 ENGRI 115 FINAL...

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ENGRI 115, Fall 2006 2 1. (15) Rupert Murdoch, the media mogul, has just told you of his plan to invest \$1.2 million in one or more of the four major entertainment companies (Artisan, Disney, Fox, Lions Gate). As his investment advisor, you are to determine which companies Mr. Murdoch should invest in and how many shares of those companies he needs to buy in order to maximize his estimated annual return. His ﬁnancial research team has provided you with the information you need to make the decision. (Disclaimer: the problem and all the numbers provided are ﬁctitious and overly simpliﬁed) Entertainment companies Stock Price per share Est. Annual return per share 1. ARTISAN \$14 \$0.98 2. DISNEY \$25 \$1.42 3. FOX \$24.5 \$2.11 4. LIONS GATE \$2.38 \$0.39 Shares can be purchased in fractional amounts, but you have to buy at least one whole share of a company if you are investing in it. Beside these data, Mr. Murdoch also gave you some additional guidelines that you need to follow: Total number of ARTISAN and DISNEY shares bought has to be greater than 5,000. You can invest in at most 3 diﬀerent companies. You can invest in either DISNEY or FOX but not both. You can invest in LIONS GATE only if you invest in ARTISAN. Formulate (do not solve) a linear IP (or Mixed linear IP) to maximize Mr. Murdoch’s annual return on investment, clearly deﬁning the variables. Soluiton: Note that here we need to decide both which stocks to buy, and for those stocks we are buying, how much to buy. Therefore, we will have two groups of variables: for each j = 1 , 2 , 3 , 4, corresponding to the four companies above, we deﬁne y j = ± 1 if some amount of stock of company j is purchased , 0 otherwise , and x j = number of shares of company j purchased . Using these variables, the return-maximization problem subject to the constraints
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## This note was uploaded on 12/25/2009 for the course ENGRI 1101 at Cornell University (Engineering School).

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115finalF06s - ENGRI 115, Fall 2006 ENGRI 115 FINAL...

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