OM CH6 Hw Q1 Please answer all sections thank you so much

customers are in different industries, different prices can be charged because of the various industry pricing structures. How production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. \begin{tabular}{|c|c|c|c|c|} \hline \multirow[b]{2}{*}{ Plant } & \multicolumn{4}{|c|}{ Customer } \\ \hline & D11 & D2a2 & D3 & D44 \\ \hline Clifton Springs & $32 & $34 & $32 & $40 \\ \hline Danville & $34 & $30 & $28 & $38 \\ \hline \end{tabular} The plant capacities and customer orders are as follows. \begin{tabular}{|l|c|} \hline Plant & Capacity (units) \\ \hline Clifton Springs & 5,000 \\ \hline Danville & 3,000 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Distributor Orders (units) } \\ \hlineD1 & 2,000 \\ \hlineD2 & 5,000 \\ \hlineD3 & 3,000 \\ \hlineD4 & 2,000 \\ \hline \end{tabular} (a) Develop a network model and a linear programming formulation of this problem. (i) network model (Submit a file with a maximum size of 1MB.) Choose File No file chosen This answer has not been graded yet. (ii) linear programming formulation Max s.t. Orders from Clifton Springs Orders from Danville Orders from/for Dummy Node Orders for D1 Orders for D2 Orders for D3 Orders for D4 xij0foralli,j. (b) How many units should each plant produce for each customer to maximize profits? (c) Which customer demands will not be met? Distributor 1 will have a shortfall of Distributor 2 will have a shortfall of Distributor 3 will have a shortfall of Distributor 4 will have a shortfall of units. units. units. units