Problem 4: Set covering problem (20 points) A troop of Canadian soldiers has recently been sent to a foreign country to support a defense mission. They were assigned to defend a region with many hills. As the hills could block the sight of the areas beneath them, the troops decided to place sentries on the hills. They were provided the following geographical map. AREAL C. AREA IV D AREA // B AREA TII AREA V E They partitioned the map into five areas, AREA I to V, and have identified five spots on the hills, A to E (the red dots) that are good for placing sentry. A sentry if placed at one of the spots can watch over the areas right beside the spot (the areas that have the spot over their boundaries). The troops have to figure out the minimum number of sentry they need to ensure each area is supervised by at least one sentry. a. Formulate this problem algebraically (i.e. define the decision variables, objective function, and constraints). Use Excel's Solver to determine the optimal solution. (Provide the corresponding Excel Spreadsheet" and the "Answer Report"). Include "managerial statements that communicate the results of the analyses, (i.e. describe verbally the results). (18 points) b. Suppose there is an additional requirement: If a sentry is placed at the spot A, then there must also be a sentry placed at the spot B or spot D. Write down the constraint algebraically. (2points)