Kaylee Fernandez came into some money from her trust fund and now has $120,000. Kaylee’s colleagues have always raved about earning a lot of money from investing in stocks and she is now interested in investing as well. She consulted an investment specialist and decided that she wants to buy some stocks in a healthcare company and a high-tech company. Kaylee has also decided that the proportion of the dollar amount she invests in the healthcare company relative to the high-tech company should at least be at least one-third, but that she should not invest more than twice the amount in the high-tech company that she invests in the healthcare company. The price per share of stock in the healthcare company is $175. The unit investment in the high-tech company is $208. The average annual return in the healthcare company during the last 3 years has been 17%. On the other hand, the high-tech company fund has been 28% for the same time period. Kaylee wants to determine a good investment strategy that will maximize her return for the coming year. Instructions: 1) Formulate the complete LP model for Kaylee. 2) Solve this problem graphically and show your graph with the feasible solution area (hand-drawn or digital graphs are okay). 3) Discuss the impact to the optimal solution if Kaylee decides to eliminate the restriction of the amount she invests in the healthcare company to the amount she invests in the high-tech company must be at least one-third.
Kaylee Fernandez came into some money from her trust fund and now has $120,000. Kaylee’s colleagues have always raved about earning a lot of money from investing in stocks and she is now interested in investing as well.
She consulted an investment specialist and decided that she wants to buy some stocks in a healthcare company and a high-tech company. Kaylee has also decided that the proportion of the dollar amount she invests in the healthcare company relative to the high-tech company should at least be at least one-third, but that she should not invest more than twice the amount in the high-tech company that she invests in the healthcare company.
The price per share of stock in the healthcare company is $175. The unit investment in the high-tech company is $208. The average annual return in the healthcare company during the last 3 years has been 17%. On the other hand, the high-tech company fund has been 28% for the same time period. Kaylee wants to determine a good investment strategy that will maximize her return for the coming year.
Instructions:
1) Formulate the complete LP model for Kaylee.
2) Solve this problem graphically and show your graph with the feasible solution area (hand-drawn or digital graphs are okay).
3) Discuss the impact to the optimal solution if Kaylee decides to eliminate the restriction of the amount she invests in the healthcare company to the amount she invests in the high-tech company must be at least one-third.
Part(1):
Given that,
Kaylee Fernandez came into some money from her trust fund and now has $120,000.
She consulted an investment specialist and decided that she wants to buy some stocks in a healthcare company and a high-tech company.
Assume that Kaylee invested amount x dollars in a healthcare company and y dollars in a high-tech company
Kaylee has also decided that the proportion of the dollar amount she invests in the healthcare company relative to the high-tech company should at least be at least one-third.
Thus, it gives
By simplifying,
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