# Maths

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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
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 -

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.

• Maths -

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 -

Sorry the symbols are showing strangely, they are greater/less than or equal to.

• Maths -

On the constraints, where did you get the figures? All I see in the problem statement is percents?

• Maths -

I converted the 250 million into figures, was that wrong?

• Maths -

I have to input the information into an initial simple tableau after.

• Maths -

I don't see anything wrong with the constraints.

• Maths -

Was I right to convert them?

When I add them into the initial simplex tableau it's filled with 1s is that normal?

• Maths -

I cannot comment on your tableau operation, I don't know them. Yes, the percents were properly converted.

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