Question

Formulate but do not solve the problem.

The management of a private investment club has a fund of $260,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high risk (x), medium risk (y), and low risk (z). Management estimates that high risk stocks will have a rate of return of 15%/year; medium risk stocks, 10%/year; and low risk stocks, 6%/year. The investment in low risk stocks is to be twice the sum of the investments in stocks of the other two categories. If the investment goal is to have a rate of return of 9% on the total investment, determine how much the club should invest in each type of stock. (Assume that all the money available for investment is invested.)

	=	260,000
	=	z
	=	23,400

Answer 1

The total fund available with the management of a private investment club to invest in stock=260,000

high risk stock investment=x,

medium risk stock investment =y,

and low risk stock investment=z

x+y+z=260000.................(1)

Its given that the investment in low risk stocks is to be twice the sum of the investments in stocks of the other two categories.

z=2(x+y)

-2x-2y+z=0.........................(2)

0.15x+0.1y+0.06z=0.09*(260000)

0.15x+0.1y+0.06z=23400......(3)

writing above equations in matrix form we get

solvimg the system of linear equations using Gaussian- elimination.

R₁ + 0.8 R₃ → R₁ (multiply 3 row by 0.8 and add it to 1 row); R₂ - 1.8 R₃ → R₂ (multiply 3 row by 1.8 and subtract it from 2 row)

high risk stock investment=x

x = 260000/3;

medium risk stock investment =y,

y= 0;

and low risk stock investment=z

z = 520000/3