Re: Linear Programming Question

On 11 Apr 2007 20:42:44 -0700, "Protoman" <Protoman2050@xxxxxxxxx>
wrote:

I have this LP problem:

You have $20K to invest in stocks, bonds, and the money market. The
stocks yield 20%, the bonds yield 10%, and the money market fund
yields 7.5%. You'll invest whatever you have left after investing in
the stocks and bonds in the MM fund. But your broker limits
investments in the fund to $10K. Fees of your broker is 20% of assets.
What is your max return?

x=stocks
y=bonds
20-x-y=MM fund

x>=0,y>=0, y>=-x+20,y>=-x+10,y<=x/5 Y=.20x+.10y+.075(20-x-y) //Y=.025x
+.125y+1.5

-x+10=x/5
-5x+50=x
-4x=-50
x=12.5
y=-2.5

We can throw this one out b/c y is negative.

-x+20=x/5
-5x+100=x
-4x=-100
x=25
y=-5

This one can also be thrown out, b/c y is also negative.

-x+10=0
x=10
y=0

(10,0)

-x+20=0
x=20
y=0

(20,0)

Y=.025(10)+.125(0)+1.5
Y=1.75

Y=.025(20)+.125(0)+1.5
Y=2

Your max return is $2,000 if you invest all of your $20,000 in stocks.

Is this correct?


Thanks!!!!

I'm not even looking at your analysis, but it seems to me that the
problem can be solved with just common sense.

Since stocks give the highest return, invest as much as possible in
stocks (i.e. 100% of available funds).

The fee is presumably deducted in advance. Then:

$20,000 [initial amount] - $4,000 [broker's fee]

leaves $16,000 to invest.

Investing $16,000 in stocks produces a profit of $3,200.

So your ending asset value is $19,200, and thus a loss of $800.

If the fee is deducted at the end, it comes out exactly the same:

Investing $20,000 in stocks produces a profit of $4,000.

So your ending asset value (before the fee is deducted) is $24,000.

$24,000 [ending asset value before fee] - $4,800 [broker's fee]

leaves $19,200 [ending asset value], and thus a loss of $800.

By the way, the fact that it came out the same either way is no
accident. In the first calculation, you are effectively multiplying
the starting amount by (1-1/5)*(1+1/5), whereas in the second,
you are multiplying by (1+1/5)*(1-1/5).

Bottom line: If you stay with this broker long enough, you will
eventually get to zero balance.

quasi
.

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