A security company has been commissioned to provide private security to five valuable assets (a1,a5). The company has currently five emplovees, as listed below: [ To provide security for an asset, two staff members should be present for the duration of the shift. Each of the staff members must work two shifts during their contracted hours. The shifts are predefined and there is only one shift available per asset, but unfortunately the shifts for protecting some assets partially overlap in time. This means that it is not possible for a single staff member to do two of them together. The pairs of assets that are incompatible are: - a2 and a4 - a4 and a5 Note that it is still fine for an employee to work both on a2 and a5 if deemed suitable. The employees have expressed their preferences for working some of these shifts as a number from 1 to 5 . Here, 5 is the most preferred and 1 is the least preferred. This is how the data looks like: Your task is to find the best possible assignment of staff to assets. Remember that each asset should get two staff members, and each staff member should be assigned two shifts, but these should not be conflicting ones. The assets to protect. It is not entirely clear to them what is the best quantity to optimise, so they are asking you to come up with a sensible measure that makes use of the preferences above. You should write a short report including the following: 1. A linear programming formulation for the above problem, with all equations numbered. Below the formulation refer to the constraints by number and briefly explain what their purpose is. The formulation must include a suitable objective function related to the preferences. In the text, justify your objective function choice and any sensible alternatives that you might have considered. 2. Implement and solve the model using the Excel solver. Include the optimal solution in your report, which should be a list with the employee names followed by the two assets they have been assigned to. 3. The company has come up with a last-minute requirement. Because Stuart is just a trainee, he should be accompanied in at least one of his shifts by Nomi, so she can provide some guidance. It is not necessary that they share both shifts, but they might do so if that works out best. Write and explain the new constraint(s) that you need to include in your model to account for this. Implement them in the Excel model and write a new solution. Write a couple of sentences explaining how this has changed the solution and why. A security company has been commissioned to provide private security to five valuable assets (a1,a5). The company has currently five emplovees, as listed below: [ To provide security for an asset, two staff members should be present for the duration of the shift. Each of the staff members must work two shifts during their contracted hours. The shifts are predefined and there is only one shift available per asset, but unfortunately the shifts for protecting some assets partially overlap in time. This means that it is not possible for a single staff member to do two of them together. The pairs of assets that are incompatible are: - a2 and a4 - a4 and a5 Note that it is still fine for an employee to work both on a2 and a5 if deemed suitable. The employees have expressed their preferences for working some of these shifts as a number from 1 to 5 . Here, 5 is the most preferred and 1 is the least preferred. This is how the data looks like: Your task is to find the best possible assignment of staff to assets. Remember that each asset should get two staff members, and each staff member should be assigned two shifts, but these should not be conflicting ones. The assets to protect. It is not entirely clear to them what is the best quantity to optimise, so they are asking you to come up with a sensible measure that makes use of the preferences above. You should write a short report including the following: 1. A linear programming formulation for the above problem, with all equations numbered. Below the formulation refer to the constraints by number and briefly explain what their purpose is. The formulation must include a suitable objective function related to the preferences. In the text, justify your objective function choice and any sensible alternatives that you might have considered. 2. Implement and solve the model using the Excel solver. Include the optimal solution in your report, which should be a list with the employee names followed by the two assets they have been assigned to. 3. The company has come up with a last-minute requirement. Because Stuart is just a trainee, he should be accompanied in at least one of his shifts by Nomi, so she can provide some guidance. It is not necessary that they share both shifts, but they might do so if that works out best. Write and explain the new constraint(s) that you need to include in your model to account for this. Implement them in the Excel model and write a new solution. Write a couple of sentences explaining how this has changed the solution and why