An Investment Fund manager is required to maximise the return on a portfolio of bonds given the following information:

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.

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.

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

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

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

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

I don't see anything wrong with the constraints.

Was I right to convert them?

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

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

To formulate the linear program in standard form to maximize the projected return, let's define some variables:

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.