Problem $2)$ Investment Strategy to Meet Clients' Needs. Innis Investments manages funds for a

number of companies and clients. The investment strategy is tailored to each client's needs. For a

new client, Innis has been authorized to invest up to $$1\mathrm{.}2$ million in two investment funds: a stock

fund and a money market fund. Each unit of the stock fund costs $$50$ and provides an annual rate

of return of $10\%$; each unit of the money market fund costs $$100$ and provides an annual rate of

return of $4\%.$

The client wants to minimize risk subject to the requirement that the annual income from the

investment be at least $$60,000.$ According to Innis's risk measurement system, each unit invested

in the stock fund has a risk index of $8,$ and each unit invested in the money market fund has a risk

index of $3$; the higher risk index associated with the stock fund simply indicates that it is the riskier

investment. Innis's client also specified that at least $$300,000$ be invested in the money market

fund. LO $2,4,5$

a$.$ Determine how many units of each fund Innis should purchase for the client to minimize the

total risk index for the portfolio.

b$.$ How much annual income will this investment strategy generate?

c$.$ Suppose the client desires to maximize annual return. How should the funds be invested?