SOLUTION: 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.

Question 1174707: 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 by Theo(13342) (Show Source): You can put this solution on YOUR website!
i'm not totally sure, but i think the problem needs to be stated as:

let a = the amount of money invested in the type A investment.
let b = the amount of money invested in the type B investment.
let c = the amount of money invested in the type C investment.

you want to maximize the return, so your objective function is:

return = .08a + .10b + .14c.
this is what you want to maximize.

your constraints are:

a + b + c <= 250000
total investment must be less than or equal to 250,000.

a >= .25 * 250000
at least one quarter of the total investment must be in type A.

b >= .25 * 250000
at least one quarter of the total investment must be in type B.

0a + .06b + .10c <= .05 * 250000
the average risk factor must be smaller than or equal to .05 * the investment.

it's that last constraint i'm not very sure about, but i couldn't think of any other way to apply it.

i used a simplex method tool to find the optimum solution.

that tool can be found at https://www.zweigmedia.com/RealWorld/simplex.html

the results of using that tool are shown below.

the results show that your maximum return on the invewtment will be 26,500.
that's the value for the variable p.

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