Question

An investor has up to $250,000 to invest in three types of investments. Type A pays 8% annually and has a risk factor of 0. Type B pays 10% annually and has a risk factor of 0.06. Type C pays 14% annually and has a risk factor of 0.10. To have a well-balanced portfolio, the investor imposes the following conditions. The average risk factor should be no greater than 0.05. Moreover, at least one-fourth of the total portfolio is to be allocated to Type A investments and at least one-fourth of the portfolio is to be allocated to Type B investments. How much should be allocated to each type of investment to obtain a maximum return?

Answer 1

objective function (return)
P=.08A+.1B+.14C
subject to the following constraints:
A+B+C<=250,000
.05>=(.06*B+.1*C)/250,000
.25*250,000>=A
.25*250,000>=B
notice that there are four contraints, but only three unknowns, so this is a non-standard LP system, so you have to use slack variables, and with this, I assume you go to some type of computational aid.
The simplex tool is here: http://www.zweigmedia.com/RealWorld/simplex.html and your problem is ....
Maximize P = .08A+.1B+.14C subject to
A + B + C <= 250000, A <= 6250, B <= 6250., 0.06B + .1C <= 12500 which is the format for inputting to the program, and the optimal solution is given

Answer 2

4. An investor has up to $250,000 to invest in three types of investments. Type A pays 8% annually and has a risk factor of 0. Type B pays 10% annually and has a risk factor of 0.06. Type C pays 14% annually and has a risk factor of 0.10. To have a well-balanced portfolio, the investor imposes the following conditions. The average risk factor should be no greater than 0.05. Moreover, at least one-fourth of the total portfolio is to be allocated to Type A investments and at least one-fourth of the portfolio is to be allocated to Type B investments. How much should be allocated to each type of investment to obtain a maximum return?