Question1In 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 wanta mixture of stocks.As a stock broker, you'll offer your clients the option to buy from a set number of well curated portfolios.In MAT 133, therearethreecorporationsthatwe'll consider:HoldenAeronautics,HossainBotanicals,andYusunCorporation. In reality, a stockbroker 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:

PortfolioA:One share of Holden Aeronautics and one share of Hossain Botanicals.

PortfolioB:One share of Hossain Botanicals.

PortfolioC:One share of Holden Aeronautics and one share of Yusun Corporation.

1.Consider a client, Parker, who would like to purchase Portfolio X consisting of the following

stocks:four shares ofHoldenAeronautics,twosharesofHossainBotanicals,andthree

sharesofYusunCorporation.Modelthis problemasalinearsystem,andshowthatis

possibleforParkertopurchasePortfolioXbybuyinganumber of your curated Portfolios

A, B, and C.

2.ShowthatParkercouldaskforanyPortfolioYandtherewouldbesomelinear

combinationofPortfoliosA, 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.