Please help provide the $.$mod and $.$dat files in AMPL for both the original problem and the variant problem Problem Statement Suppose you manage a manufacturing plant that produces $450$K of Personal Computers per week, and two distribution centers. The two distribution centers are located in the northeast and southeast, and they receive computers from the manufacturing plant. The distribution centers transship them to warehouses located in the following cities: Boston, Newark, Baltimore, Atlanta, and Orlando. A network representation, including the cost and capacity of each arc, can be seen below. The numbers outside of the nodes are production amount $($for PITT$)$ and demand $($for each city$).$ The objective is to formulate and code in AMPL the optimization problem that minimizes the total cost and satisfies the total demand of the customer. The formulation for this problem is as follows: Parameters : Set of cities : Set of arcs : Capacity on the arc $(,)$ in : Cost to transfer one unit of product from city to city on the arc $(,)$ in $()$: Supply if $()>0$ in and demand if $()<0$ in Decision variables : Number of products shipped from city in to city in Constraints $$:$(,)$ in $$:$(,)$ in $=()$ in $0<=<=(,)$ in Objective function $($maximize the profits$)$ Minimize $(,)$ in In order to help you code the $.$mod and $.$dat files, here are the components of the $.$dat file. Additionally, here is a hint for building the $.$mod file: Lab Instructions Code the $.$mod and $.$dat files in AMPL. Solve this initial problem and report the optimal solution and optimal objective function value. Model, code, and solve the following variant to this network problem. Suppose there is a failure in one of the production lines leading to the reduction in capacity to $400$K Personal Computers. Now, you will not be able to satisfy the demand of all your customers. There is a cost per unit for not satisfying the demand of your customer, as found in the table below. Formulate and code this new variant to minimize the total cost. Indicate which cities have unsatisfied demand. City Cost per Unit Boston $11\mathrm{.}5$ Newark $12\mathrm{.}5$ Baltimore $11\mathrm{.}5$ Atlanta $11$ Orlando $13$