Consider the following integer linear programming model:Max Z = 5x1 + 6x2Subject to:17x1 + 8x2 ≤ 1363x1 + 4x2 ≤ 36x1, x2 ≥ 0 and integerWhat is the value of the objective function at the optimal solution?Hint: develop a simple integer programming model in Excel to solve this problem.

To solve this problem, you can use Excel's Solver tool. Here are the steps:

1. Open Excel and create a new worksheet.
2. In cells A1 and B1, type "x1" and "x2" respectively. These will be your decision variables.
3. In cells A2 and B2, type "0". These will be the initial values of your decision variables.
4. In cell C1, type "Z". This will be your objective function.
5. In cell C2, type "=5A2+6B2". This is the formula for your objective function.
6. In cells A4 and B4, type "17" and "8" respectively. In cell C4, type "<=136". This is your first constraint.
7. In cells A5 and B5, type "3" and "4" respectively. In cell C5, type "<=36". This is your second constraint.
8. Go to "Data" > "Solver". Set your objective to cell C2, to be maximized.
9. Add your decision variable cells (A2 and B2) in the "By Changing Variable Cells" box.
10. Add your constraints (A4:C4 and A5:C5) in the "Subject to the Constraints" box.
11. Check the "Make Unconstrained Variables Non-Negative" box and select "Simplex LP" as the solving method.
12. Check the "Integers" box to ensure that your decision variables are integers.
13. Click "Solve".

The optimal solution will be displayed in cells A2 and B2, and the value of the objective function at the optimal solution will be displayed in cell C2.

To solve this problem, you can use Excel's Solver tool. Here are the steps:

1. Open Excel and create a new worksheet.
2. In cells A1 and B1, type "x1" and "x2" respectively. These will represent your decision variables.
3. In cells A2 and B2, type "0". These will be the initial values for your decision variables.
4. In cell C1, type "Z". This will represent your objective function.
5. In cell C2, type "=5A2+6B2". This is the formula for your objective function.
6. In cells A4 and B4, type "17" and "8" respectively. In cell C4, type "<=136". This represents your first constraint.
7. In cells A5 and B5, type "3" and "4" respectively. In cell C5, type "<=36". This represents your second constraint.
8. Go to "Data" tab, click on "Solver" in the "Analysis" group. If Solver is not there, you need to add it in by going to File -> Options -> Add-Ins -> Excel Add-Ins -> Solver Add-In.
9. In the Solver Parameters dialog box, set the objective to cell C2, set the "To" option to "Max", and add the constraints as they are listed in the problem.
10. In the Solver Parameters dialog box, check the box that says "Make Unconstrained Variables Non-Negative" and select "Int" from the "Select a Solving Method" dropdown menu to ensure that the solution only includes integers.
11. Click "Solve".

The optimal solution will be displayed in cells A2 and B2, and the maximum value of the objective function will be displayed in cell C2.