q1.

High Return Investment Inc. provides its clients with a host of investment portfolios. Currently, one of its customers, Jim Wealthy, approaches the company with a fund of $400,000 . Jim hopes that all money is invested and the company provides four mutual funds with different focuses to diversify Jims portfolio. The relevant data are provided in the table.

High Return Investment Inc.s top management has stipulated the following guidelines after consulting with Jim:

a)The annual rate of return for the portfolio must be at least 9%;

b)No single mutual fund can account for more than 40% of the total dollar invested;

c)The amount invested in International cannot exceed 15% of the total amount in the other three funds;

d) To diversify the investment, at least 50% of the money should be invested in US Equity and International fund.

The objective is to minimize the risk of the portfolio while all the aforesaid constraints are satisfied.

		Mutual Fund
		Canadian Equity	Dividend	US Equity	International
Price per unit		30	45	25	15
Annual rate of return		0.12	0.08	0.06	0.14
Risk measure per unit invested		0.11	0.05	0.07	0.15

q2.

As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the annual payments (in thousands of dollars) shown in Table 1.

The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the funds will be limited to savings and two government securities shown in Table 2. All three are availible to invest at the beginning of every year.

During the first 2 years (i.e., Year 1 and Year 2),

a) the average risk index of invested funds cannot exceed 3;

b) the average years to maturity at the beginning of each year cannot exceed 2.5.

There are no risk or liquidity requirements for Years 3 to 6.

Solve this LP to minimize the initial amount needed.

Year	1	2	3	4	5	6
Payment	190	215	240	285	315	460

Investment	Yield (%) at Maturity	Years to Maturity	Risk Index
Savings (SV)	1.5	1	1
Security A (SA)	6.5	3	2
Security B (SB)	11	4	4