Innis Investments manages funds for a number of companies and wealthy 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.

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