Please use AMPL software to code this problem. Do not use Python, C++, Etc.

Please provide a .dat file and .mod file for the original problem.

Please also provide a separate .dat and .mod file for the variant problems.

Suppose that you manage a chain of retail stores that sell only one product. Customers place orders online and, after processing the payment, you need to decide which store will satisfy the demand of each customer (orders must be satisfied by one store). Stores have a limited produce inventory and the shipping cost depends on the distance to the customer.

Store	Inventory
1	10
2	12
3	5
4	5
5	20

Customer	Demand	Shipping Cost ($ / unit)
		Store 1	Store 2	Store 3	Store 4	Store 5
1	1	1	2	3	1	5
2	5	2	3	4	5	7
3	5	1	3	2	1	1
4	2	1	2	1	3	5
5	10	1	2	1	4	5
6	2	1	2	1	3	2
7	4	1	4	3	1	5
8	6	4	1	2	1	3
9	2	2	1	2	1	2
10	1	3	1	3	4	2

Instructions

• Using AMPL Code and solve this retail problem (use the formulation provided).
• Report the allocation of customers to stores and the total cost of this plan.
• Model, code, and solve the following variants to this retail problem (variants are independent and should be implemented separately).
  • Variant 1: Demands can be satisfied by multiple stores (i.e., a customer can receive units from multiple stores).
  • Variant 2: Stores can request no more than 10 additional units from a nearby warehouse at a flat cost of p_j, shown in the table below.

Store	pj
1	3
2	4
3	0.5
4	0.5
5	5

1. Parameters J : set of stores - I : set of customers cij : shipping cost from store jJ to customer iI di : demand of customer iI kj : product inventory in store jJ 2. Decision variables - yij : binary variable: 1 if customer iI is served by store jJ;0 otherwise 3. Constraints jJyij=1iIiIdiyijkjjJyij{0,1}iI,jJ 4. Objective function - Minimize iIjJdicijyij