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.
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0. Type B pays 10% annually and has a risk factor of 0.06.
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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):
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.
