Innis Investments manages funds for a number of companies and wealthy clients. Theinvestment strategy is tailored to each client's needs. For a new client, Innis has beenauthorizedtoinvestuptoRM1.2millionintwoinvestmentfunds:astockfundandamoneymarketfund.EachunitofthestockfundcostsRM50andprovidesanannualrateofreturnof 5%; each unit of the money market fund costs RM100 and provides an annual rate ofreturnof4%.

The client wants to minimize risk subject to the requirement that the annual income fromtheinvestmentbeatleastRM60,000.AccordingtoInnis'sriskmeasurementsystem,eachunit invested in the stock fund has a risk index of 8, and each unit invested in the moneymarket fund has a risk index of 3; the higher risk index associated with the stock fundsimply indicates that it is the riskier investment. Innis's client has also specified that atleastRM300,000 be invested inthemoneymarketfund.

Inherinvestmentplan,Innishastofollowtheclientrequesttominimizethetotalriskindexfortheportfolio investment.

1. LetX1=unitspurchasedinthestockfundandX2=unitspurchasedinthemoneymarket,formulatethe LPProgramming.

1. SolvetheLPProgrammingproblemusingQMforWindows.Whatistheoptimalsolution, andwhatistheminimumtotalrisk?

1. Whatis therateofreturnfortheportfolio?

1. Whatarethedualpricesfortheconstraints?Interpreteach.

1. Supposetheriskindexforthestockfundincreasesfromitscurrentvalueof8to12.Wouldthesolution change? Justifyyouanswer.