A fund manager has P 10 million to invest in treasury bills, bonds, private placements and in risky venture. Relevant information about these various investments are presented below:

Investment	Yield rate p.a.	Maturity	Risk rating
Treasury Bill	6%	3 months	1
Bonds	8%	5 years	2
Private Placement	12%	6 months	4
Risky Venture	20%	3 years	8

Guidelines given by the fund manager were:

1. 50% of the investment must have a maturity below one year

2. Investment in Risky venture should not exceed 20% of funds invested.

3. At least 30% should be invested in treasury bills.

4. Total investments in items risk rating above 3 should not exceed 40% of total funds invested.

Formulate an LP model that would optimize return for this portfolio where X1 = investment in Treasury bills, X2 = investment in bonds, X3 = investment in private placement, X4 = investment in risky venture