Question$-4-$ The Agrawal Inc., a mid$-$sized manufacturing firm, is currently optimizing its distribution network to reduce shipping costs of products. The company operates three production plants located in cities $\backslash (\backslash$mathrm$\{$A$\},\backslash$mathrm$\{$B$\}\backslash ),$ and C $.$ To streamline distribution, products are first sent to two warehouses, D or E $,$ before being delivered to their final destinations. The end customers, W$,$ X$,$ Y$,$ and Z$,$ have specific demands that must be met efficiently.

Given the varying transportation costs between the plants, warehouses, and customers, The Agrawal Inc. wants to develop a cost$-$effective distribution plan. The goal is to determine how much product should flow from each plant to each warehouse and then from each warehouse to the customers, minimizing total shipping expenses. The supply capacity of each plant, demand from each customer, and unit shipping costs are detailed in the table below. Your task is to set up and solve the transshipment model to find the optimal shipping plan, costs, etc. $(10$ Marks$)($CO$2)$

Supply and demand data for The Agrawal Inc. $-$

Transportation costs for The Agrawal Inc. $-$