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April 19, 2015

Posted by **Sarah** on Tuesday, December 8, 2009 at 6:43am.

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 8:02amPlease 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 8:28amMax 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 8:37amSorry the symbols are showing strangely, they are greater/less than or equal to.

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

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

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

- Maths -
**bobpursley**, Tuesday, December 8, 2009 at 9:59amI dont see anything wrong with the constraints.

- Maths -
**Sarah**, Tuesday, December 8, 2009 at 10:03amWas 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 10:12amI cannot comment on your tableau operation, I dont know them. Yes, the percents were properly converted.