Formulate the LP and Solve Using Excel, use this template

Problem 1 (5 pts): Health Facility Location in the Belt Background: Belters play a vital role in supplying resources to both Earth and Mars. The Belt's leadership is contemplating establishing medical facilities in key locations to tend to Belters' unique health needs, given their adaptation to low-gravity environments. The challenge is to decide where to establish these facilities to ensure maximal coverage for Belters at the minimum cost. Three potential locations have been identified for the medical facilities: Ceres, Pallas, and Vesta. There are five major communities of Belters that need service: Hygea, Interamnia, Juno, Psyche, and Davida. A facility at each of the potential locations has a fixed setup cost and variable costs depending on the number of Belters it services. The following table displays the setup costs: The following table illustrates each community's service needs and the servicing cost from each facility: Please do the following: - Formulate the LP in algebraic form to solve this problem. - Solve the LP and provide the solution. \begin{tabular}{|c|c|c|c|c|c|c|} \hline \multirow[b]{2}{*}{ Plant } & \multicolumn{4}{|c|}{ Warehouse } & \multirow{2}{*}{\multicolumn{2}{|c|}{\begin{tabular}{ll} Vehicles & Max Vehicles Selection Shipped - \\ Shipped & Shipped Constraints Selection \end{tabular}}} \\ \hline & A & B & C & D & & \\ \hline 1 & 1 & 1 & 1 & 1 & & \\ \hline 2 & 1 & 1 & 1 & 1 & & \\ \hline 3 & 1 & 1 & 1 & 1 & & \\ \hline 4 & 1 & 1 & 1 & 1 & & \\ \hline 5 & 1 & 1 & 1 & 1 & & \\ \hline \multicolumn{7}{|c|}{ Vehicles shipped } \\ \hline Demand & & & & & & \\ \hline \end{tabular} \begin{tabular}{|c|cr|} \hline Plant & \begin{tabular}{c} Selection \\ ( Yi ) \end{tabular} & \begin{tabular}{c} Annual \\ Fixed Cost \end{tabular} \\ \hline 1 & 1 & ### \\ 2 & 1 & $850,000 \\ 3 & 1 & ### \\ 4 & 1 & ## \\ 5 & 1 & $900,000 \\ \hline \end{tabular} \begin{tabular}{|c|cccc|} \hline & \multicolumn{5}{|c|}{ Warehouse } \\ Plant & A & B & C & D \\ \hline 1 & $56 & $21 & $32 & $65 \\ 2 & $18 & $46 & $70 & $35 \\ 3 & $12 & $71 & $41 & $52 \\ 4 & $30 & $24 & $61 & $28 \\ 5 & $45 & $50 & $26 & $31 \\ \hline \end{tabular} \begin{tabular}{l|l|} \hline Trans. Costs & \\ Annual Fixed Cost \\ Total cost \end{tabular}