# linear programming problem

• Mar 9th 2010, 03:11 AM
linear programming problem
You are an Independent Computing Financial Advisor providing independent expert advice to individuals on request. A client has £130,000 which she wishes to invest in income-generating shares and government bonds so as to maximise her annual income. She has selected five possible investments, all of which she considers to have reasonably high levels of income and security:

·Unit trust A, with an expected annual return of 9% pa.
·Unit trust B, with an expected annual return of 7.7% pa.
·FTSE 100 share A, paying an anticipated 5% annual dividend.
·FTSE 100 share B, paying an anticipated 6.2% annual dividend.
·Gilts (Government bonds) paying 5.5% annual interest.

Since she has no plans to sell her investments in the near future, she is not concerned with their capital value (i.e. their selling price). Based on the various risk levels involved, she has made the following decisions:

·The total investment in unit trusts may not exceed £50,000.
·The total investment in FTSE 100 shares may not exceed £45,000.
·The investment in unit trust A may not exceed £25,000.
·The investment in FTSE 100 share A may not exceed £30,000.
·The total investment in unit trusts may not exceed the total investment in FTSE 100 shares.
·The investment in unit trust A and FTSE 100 share A combined may not exceed the investment in Gilts.

As the client’s financial adviser you should advise her of the amount of money she should invest in the various investments in order to maximise her annual income.

• Mar 9th 2010, 05:49 AM
Robb
Had a play in excel using solver, but basically;

You want to invest as much as possibly in the Unit trusts, where the maximum you can invest is 45000 (limited by the fact that investment in unit trusts must not exceed investments in FTSE shares).
So you invest 25000 in trust A since it returns the highest level, then the remaining 20000 in trust B since it is the second highest.

You then must invest 45000 in shares in order for the condition above to hold, so you invest it all in Share B since its return is higher then that of A.

So that leaves 40,000 to invest, which all goes into the Gilts and ensures the condition that you invest at least as much in Gilts as you do in Unit Trust A, or share A. So the portfolio is;
Unit Trust A: 25000
Unit Trust B: 20000
Share A: 0
Share B: 45000
Gilts: 40000

SO total return on this portfolio is $\displaystyle 25000\cdot 0.09 + 20000\cdot 0.077 + 45000 \cdot 0.062 + 40000 \cdot 0.055=8780$
• Mar 9th 2010, 01:10 PM