Posted by Sarah on Tuesday, December 8, 2009 at 6:43am.
An Investment Fund manager is required to maximise the return on a portfolio of bonds given the following information:
Bond types Projected rate of return
Benchmark government 9.1
UK gilts 10.3
Global investment grade (US $) 6.7
Global investment grade (euro) 8.7
Global investment grade (£) 5.9
High yield emerging market 8.8
The limitations imposed on the fund manager are:
(i) The sum of Global investment grade (US $) and global investment grade (£) bonds cannot be less than 30% of the total investment.
(ii) Global investment grade (euro) is required to be no more than 20% of the total investment.
(iii) The sum of Benchmark government, UK gilts and high yield emerging market bonds must account for at least 40% but no more than 50% of the total investment.
(iv) The sum allocated to the portfolio is £250 million.
(v) The sum of Global investment grade (US $) and global investment grade (£) cannot exceed 50% of the total investment.
(a) Formulate the linear programme in standard form to maximise the projected return.

Math  Writeacher, Tuesday, December 8, 2009 at 8:02am
Please understand that no one here will do your work for you. However, we will be happy to read over whatever you come up with and make suggestions and/or corrections.
Please post what you think, and someone might be able to help you.

Maths  Sarah, Tuesday, December 8, 2009 at 8:28am
Max Z = 9.1x1 + 10.3x2 + 6.7x3 +8.7x4 + 5.9x5 + 8.8x6
Subject to:
x3 + x5 ¡Ý 750,000
x3 + x5 ¡Ü 1,500,000
x4 ¡Ü 500,000
x1 + x2 + x6 ¡Ý 1,000,000
x1 + x2 + x6 ¡Ü 1,500,000
I feel the constraints are wrong. The next question requires you to set up the initial simplex tableau and the constraints then don't make sense.

Maths  Sarah, Tuesday, December 8, 2009 at 8:37am
Sorry the symbols are showing strangely, they are greater/less than or equal to.

Maths  bobpursley, Tuesday, December 8, 2009 at 9:33am
On the constraints, where did you get the figures? All I see in the problem statement is percents?

Maths  Sarah, Tuesday, December 8, 2009 at 9:49am
I converted the 250 million into figures, was that wrong?

Maths  Sarah, Tuesday, December 8, 2009 at 9:54am
I have to input the information into an initial simple tableau after.

Maths  bobpursley, Tuesday, December 8, 2009 at 9:59am
I don't see anything wrong with the constraints.

Maths  Sarah, Tuesday, December 8, 2009 at 10:03am
Was I right to convert them?
When I add them into the initial simplex tableau it's filled with 1s is that normal?

Maths  bobpursley, Tuesday, December 8, 2009 at 10:12am
I cannot comment on your tableau operation, I don't know them. Yes, the percents were properly converted.
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