Question 1 In this question, you will consider the role of a stock portfolio broker. When designing a stock portfolio, it is important to diversify your holdings so as to distribute risk and growth. Ideally, you want a mixture of stocks. As a stock broker, youll offer your clients the option to buy from a set number of well curated portfolios. In MAT 133, there are three corporations that well consider: Holden Aeronautics, Hossain Botanicals, and Yusun Corporation. In reality, a stock broker would manage portfolios with hundreds or thousands of stocks.

After extensive research, and forecasting, it has been determined that the following portfolios have a good mixture of risk and growth:

Portfolio A : One share of Holden Aeronautics and one share of Hossain Botanicals.

Portfolio B : One share of Hossain Botanicals.

Portfolio C : One share of Holden Aeronautics and one share of Yusun Corporation.

(please answer all three parts 1-3!)

1. Consider a client, Parker, who would like to purchase Portfolio X consisting of the following stocks: four shares of Holden Aeronautics, two shares of Hossain Botanicals, and three shares of Yusun Corporation. Model this problem as a linear system, and show that is possible for Parker to purchase Portfolio X by buying a number of your curated Portfolios A, B, and C.

2. Show that Parker could ask for any Portfolio Y and there would be some linear combination of Portfolios A, B, C which would add up to Portfolio Y.

3. What happens if Parker asks for a portfolio consisting of a single share of Holden Aeronautics? Discuss whether or not your answer is financially reasonable.