NEED HELP with Quantitative Methods Linear Programming Model!!!!!!!!!!

[svkalland]

I am so confused by how to even find the constraints for this maximization problem. Any help would be wonderful.

There is $800,000 to be invested, between three funds: money market, growth, and income. The suggested investment guidelines are: Growth 20%-40%, income 20-50%, and money market needs to be at least 30% of the total funds. The maximum risk index for the company with the $800,000 investment is 0.05. The risk of the growth fund is 0.1, the income fund is0.07, and the money market fund is 0.01. Recommend how much of the $800,000 should be invested in each of the three funds. What is the annual yield you anticipate for the investment recommendation?

 

[tkhunny]

A piece at a time. Staying organized is the hardest part. I'll give you one for free. You have to do the next one and show us what you get.

#1 - Name Stuff

M = Amount Invested in Money Markets
G = Amount Invested in Growth
I = Amount Invested in Income

"There is $800,000 to be invested"

M + G + I = 800000 (You may need a giant and painful slack variable for this equality)

"Growth 20%-40%"

0.20 <= G/800000 <= 0.40 Which you may wish to rephrase as 160000 <= G <= 320000

"income 20-50%"

0.20<= I/800000 <= 0.50 Rephrase...

"money market needs to be at least 30%"

M/800000 >= 0.30 Again, rephrase...

"The maximum risk index for the company with the $800,000 investment is 0.05. The risk of the growth fund is 0.1, the income fund is0.07, and the money market fund is 0.01."

G*0.10 + I*0.07 + M*0.01 <= 800000*0.05 = 40000

Solve away. You've seven inequalities to aid you on your search.

 

[svkalland]

Thanks!

Thanks, this is a big help. I still do not understand what the model is for the problem - is it: Max. M+G+T? If so,

Maximize (Max.) M+G+T
subject to (s.t.)

G >=160,000
G<=320,000
I >= 160,000
I <=400,000
M >=240,000
.1G+.07I+.01M <=40,000

Later in the paragraph it states that the forecasting annual yields for Growth is 18%, for Income is 12.5%, and for Money Market is 7.5%. I didnt mention it because I thought it was for a later question but now I was thinking that if the upper objective function isnt right, perhaps this is:

Max. .18G +.125I + .075M ?? This seems like it would make sense too. So lost.

 

[tkhunny]

ou cannot maximize G + I + M, since that is already 800000.

Max. .18G +.125I + .075M ?? This seems like it would make sense too.

There you have it. As you noticed, I did not provide that because you didn't provide the rates.

So lost.

No, you're not. There is nothing there you could not have done if you had not gone into the panic zone. Don't do that.

Don't forget M <= 0.6*800000. (WHY?) It may be redundant, but you should at least think about it.