Linear Prgramming

[rr2013]

Can someone please help me with this question I think I'm stuck

Blue Bell Corp has 20m to invest:
investment rate of return% risk score
trade credits 9 1.7
corporat bonds 12 1.2
gold stocks 16 3.7
platinum stocks 10 2.4
mortgage sec. 6 2.0
construction loans 16 2.9

cannot invest more than 20% in any one investment, at least 30% in pr
ecious stones and metals at least 45% in trade credits and corp. bonds, overall risk no more than 2.0

 

[JeffM]

Can someone please help me with this question I think I'm stuck

Blue Bell Corp has 20m to invest:
investment rate of return% risk score
trade credits 9 1.7
corporat bonds 12 1.2
gold stocks 16 3.7
platinum stocks 10 2.4
mortgage sec. 6 2.0
construction loans 16 2.9

cannot invest more than 20% in any one investment, at least 30% in pr
ecious stones and metals at least 45% in trade credits and corp. bonds, overall risk no more than 2.0

How can we see where you are stuck and how to get you unstuck if we do not see what you have done so far? We are not mind readers. How have you named your variables? What is your objective? So have you defined an objective function? If so, what is it? What constraining inequalities have you identified? What are they? Is there any discussion in the problem how overall risk of a portfolio is to be determined?

 

[HallsofIvy]

Start by naming things. Let "A" be the amount of money invested in "trade credits", "B" the amount of money invested in "corporate bonds", "C" the amount of money invested in "gold stocks", "D" the amount of money invested in "platinum stocks", "E" the amount of money invested in "mortgage sec." and "F" the amount of money invested in "construction loans", each in millions of dollars.

"Blue Bell Corp has 20m to invest" so \(\displaystyle A+ B+ C+ D+ E+ F\le 20\).
"cannot invest more than 20% in any one investment" so \(\displaystyle A\le .2(20)= 4\), \(\displaystyle B\le 4\), etc.
"at least 30% in precious stones and metals" so \(\displaystyle C+ D\ge .3(20)= 6\) a
"at least 45% in trade credits and corp. bonds" so \(\displaystyle A+ B\ge .45(20)= 9\)
and "overall risk no more than 2.0". I am not absolutely sure how "overall risk" would be calculated but I suspect a weighted average: \(\displaystyle \frac{1.7A+ 1.2B+ 3.7C+ 2.4D+ 2.0E+ 2.9F}{A+ B+ C+ D+ E+ F}\le 2.0\).
And the object function is .09A+ .12B+ .16C+ .10D+ .06E+ .16F.

 

[rr2013]

Thanks A lot!!!!