Linear Programming - Investment Strategy

[Jademonkey]

How can I set this question up?

Client has 800,000 that must be invested in 3 funds:

. . .20% to 40% invested in growth fund
. . .20% to 50% invested in income fund
. . .at least 30% invested in money market fund

Client has a max risk index of 0.05. Risk indicators:

. . .growth fund is 0.10
. . .income fund is 0.07
. . .money market is 0.01

Portfolio risk index is computed as a weighted average of risk rating for the three funds where the weights are the fraction of the clients portfolio invested in each of the funds. Yields are:

. . .growth - 18%
. . .income fund - 12.5%
. . .money market - 7.5%

Maximize the Yield

 

[Denis]

G: 248,800  .10   18.0
I: 160,000  .07   12.5
M: 391,200  .01    7.5
=========================
P: 800,000  .05   11.7655

 

[Jademonkey]

What constraints did you use to get that result? Its mainly the risk constraint that I am having trouble with.

 

[Denis]

What constraints did you use to get that result? Its mainly the risk constraint that I am having trouble with.

Constraints? The ones specified in your problem.

 

[Jademonkey]

Portfolio risk index is computed as a weighted average of risk rating for the three funds where the weights are the fraction of the clients portfolio invested in each of the funds. Growth = 0.1, Income = 0.07 Money Market = 0.01

What is the equation for the above constraint? To get the solution, I have to input a constraint for risk, and I am having trouble getting that.

 

[Denis]

(.10G + .07I + .01M) / 800000 =< .05 (where G + I + M = 800000, of course)

 

[Jademonkey]

thank you! im not sure why I was having so much trouble with that, I think I just confused myself doing this and a finance assignment at the same time.