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Use the Excel-Solver plug-in to solve the programming model given below.

**Investment Problem:**

Mr. Ayhan wants to optimize his investment of 160 million TL using the following investment options with their respective annual returns:

- Ege Fertilizer: annual return 30%
- Fertilizer Factories: annual return 22.2%
- Textile Company: annual return 28%
- A Energy: annual return 18.5%
- Z Energy: annual return 10.9%
- Treasury Bills: annual yield 24%
- Bank: annual net interest rate 22%

**Investment Constraints:**

1. The total investment in the fertilizer sector shall not exceed 60 million TL.
2. The total investment in the energy sector will not exceed 80 million TL.
3. The investment in the textile sector will be at most 8 million TL.
4. Ege Fertilizer investment will be at most 40 million TL.
5. The total investment in the fertilizer and textile companies should be less than that in the energy companies.
6. The total investment in Treasury Bills and the bank should be at least 30 million TL.
7. The maximum amount invested in energy will be 50 million TL.
8. The investment in Aegean fertilizer and textile, Treasury Bills, and bank interest should be less than the invested amount.

**Programming Model:**

Maximize:

\[ \text{Zmaks} = 0.30x_1 + 0.222x_2 + 0.28x_3 + 0.185x_4 + 0.109x_5 + 0.24x_6 + 0.22x_7 \]

Subject to:

\[ x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 = 160 \] (Total investment amount)

\[ x_1 + x_2 \leq 60 \] (1st constraint)

\[ x_4 + x_5 \leq 80 \] (2nd constraint)

\[ x_3 \leq 8 \] (3rd constraint)

\[ x_1 \leq 40 \] (4th constraint)

\[ x_1 + x_2 + x_3 - x_4 - x_5 \leq 0 \] (5th constraint)

\[ x_6 + x_7 \geq 30 \] (6th constraint)

\[ x_4 \leq 50 \] (7th constraint)

\[ x_1 + x_3 - x_6 - x_7 \leq 0 \] (8th constraint)

\[ x_1, x_2, x_3, x_4, x_5, x_6, x_7 \geq 0 \]

Determine the type of investment and the amount to invest using the Microsoft Excel Solver add-in.

Answer :

Final answer:

Mr. Ayhan's investment problem can be solved using the Solver plug-in in Microsoft Excel by setting up the given programming model and adding the constraints as given in the question. This will maximize Mr. Ayhan's investment returns given the rules he has set

Explanation:

Given the programming model, you can make use of the Microsoft Excel Solver add-on to help Mr. Ayhan make the most efficient investments. These calculations would have to be performed in accordance with the limitations that Mr. Ayhan has set for each individual investment.

The Solver function in Excel can maximize or minimize certain outcomes, which, in this case, could be Mr. Ayhan's investment returns. To use the Solver function in excel, go to the 'Data' tab, and choose 'Solver' which is under 'Analysis'. Enter the target cell, which, in this case, would be the cell representing the total return. The changing cell would be the amount to invest in each. You also need to add constraints that correspond to Mr. Ayhan's decisions, which would be as explained in the question.

By solving this Linear Programming problem using the Microsoft Excel Solver add-on, we can find the optimal investment strategy that abides by the rules set forth by Mr. Ayhan and uses his capital most effectively.

Learn more about Investment returns here:

brainly.com/question/33850942

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