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.
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.
Please post what you think, and someone might be able to help you.
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.
When I add them into the initial simplex tableau it's filled with 1s is that normal?
Let x1 represent the amount invested in Benchmark government bonds.
Let x2 represent the amount invested in UK gilts.
Let x3 represent the amount invested in Global investment grade (US $) bonds.
Let x4 represent the amount invested in Global investment grade (euro) bonds.
Let x5 represent the amount invested in Global investment grade (£) bonds.
Let x6 represent the amount invested in High yield emerging market bonds.
To maximize the projected return, we want to maximize the sum of (x1 * 9.1) + (x2 * 10.3) + (x3 * 6.7) + (x4 * 8.7) + (x5 * 5.9) + (x6 * 8.8).
Now, let's consider the limitations imposed on the fund manager:
(i) The sum of Global investment grade (US $) and Global investment grade (£) bonds cannot be less than 30% of the total investment.
This can be expressed as: (x3 + x5) ≥ 0.3 * (x1 + x2 + x3 + x4 + x5 + x6).
(ii) Global investment grade (euro) is required to be no more than 20% of the total investment.
This can be expressed as: x4 ≤ 0.2 * (x1 + x2 + x3 + x4 + x5 + x6).
(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.
This can be expressed as: (x1 + x2 + x6) ≥ 0.4 * (x1 + x2 + x3 + x4 + x5 + x6) and (x1 + x2 + x6) ≤ 0.5 * (x1 + x2 + x3 + x4 + x5 + x6).
(iv) The sum allocated to the portfolio is £250 million.
This can be expressed as: x1 + x2 + x3 + x4 + x5 + x6 = 250.
(v) The sum of Global investment grade (US $) and Global investment grade (£) cannot exceed 50% of the total investment.
This can be expressed as: (x3 + x5) ≤ 0.5 * (x1 + x2 + x3 + x4 + x5 + x6).
Now, we have the objective function and the set of constraints to formulate the linear program in standard form to maximize the projected return.