Formulate but do not solve the problem The management of a p

Formulate but do not solve the problem. The management of a private investment club has a fund of $120,000 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.)

______= 120,000

______= z

______= 10,800

Solution

The investment in low risk stocks is is twice the sum of investments in the high risk and medium risk categories. Therefore, z = 2(x + y). The total investment is $ 120,000. Therefore x + y + z = 120,000 or, x + y + 2(x +y) = 120,000 or, 3 (x + y) = 120000. Also 9 % of 120,000 is 10,800 and since the total investment is x + y + z, and the rate of return on x, y, z are 15 %, 10 % and 6 % respectively, we have x*15 % + y*10% + z * 6 % = 120,000*9 % or, 0.15x+ 0.10y+ 0.06z = 10,800.

Thus the answers are,

x + y + z = 120,000,

2(x+y) = z and

0.15x + 0.10y + 0.06z = 10,800

NOTE: If we want, we can replace z by 2 (x + y) in the 1st and the 3rd of the abobe answers.