1. Suppose the total investment is Q (Q = $80,000), and opening one temporary vaccination site will cost UMD f (f = $12,000). All students, staff, and faculty must access a vaccination site with a 10-minute walk (critical time). Determine the minimum number of vaccination sites that need to be opened to cover all demands while not exceeding the total investment. For this problem, assume that the vaccination sites can handle as many people as assigned (unlimited capacity). For the completion of this project, you need to do the following tasks for each problem: 1. Formulate the problem as a mathematical programming model. . State the assumptions you have made. Define appropriate notations. You must not use any abbreviation or notation before defining it. . Write the formulation, including the objective function and constraints. 2. Use one of the solvers taught in class (Matlab, Xpress) or the other solvers if you prefer (e.g., Gurobi, CPLEX) to solve the problem. Report the computational results, including: 3. . Model running time. Optimal gap (if not solved to optimality). The total number of vaccination locations. The assignment of the demand nodes to the vaccination locations. 4. Manually check whether the solutions derived from the solver are correct, for example: . The health center must be selected under each condition. All demand should be covered (For Problem 1, 2, and 4). Each selected vaccination site can only serve the demand nodes located within the critical time. The total investment in Problem 1 and 2 is not exceeded. The total number of vaccination sites can only be two in Problem 3. The capacity of each vaccination site is not exceeded (for Problem 4). 5. Compare the results from different problems and demonstrate the differences (if they exist). 6. Make a recommendation to UMD regarding the objective to use and the final vaccination site opening plan. .