Formulate the problem to determine the facilities need to be opened in order to maximize the total profit of the company. Please provide a mathematical description of the model.

Follow the formulation in Part I and solve this problem using MPL as a Mixed Integer optimization problem.

A company wishes to produce two different products. We label these products as P1 and P2. In order to produce and deliver the products to their three major customers, named as C1, C2, and C3, the company plans to re-design its global supply chain network. Each product is manufactured in a factory shipped to a warehouse, and then delivered to a customer. The company sometimes buys the finished product directly and shipped to the customer which they called "outsource". The company has identified three candidate factory locations, named as M1, M2 and M3, and three candidate warehouse locations, named as W1, W2 and W3. They can open more than one factory or warehouse. If we plan to open any facility, the fixed cost is listed as follows M1 650,000 M2 950,000 M3 550,000 W1 250,000 W2 400,000 W3 200,000 Opening cost ($) The detailed data of the shipping cost is listed as follows. P2(S) M1 M2 M3 P2(S) W1 W2 W3 W1 W2 W3 M1 M2 M3 P1S)C1 C2 C3 W1 W2 W3 Each candidate facility has a capacity limitation (labor hrs in total.) and is specified as follows. 4 25 6 4 8 10 83 C1 C2 C3 2 13 8 6 9 8 76 M1 400,000 M2 600,000 W2 750,000 W3 410,000 W1 Labor hrs 450,000 450,000 The resource consumption rate (labor hrs per product) is as follows M1 M2 M3 W1 W2 W3 P1 2 P2 3 The variable cost per product in a facility and the outsource cost are listed as follows. P1 2 P2 3 VariableW1 W2 W3 cost Outsource C1 C2 C3 Cost ($) Variable M1 M2 M3 5 3 6 7 45 97 12 P1 P2 The customer demand and unit profit per product is as follows 49 47 50 64 62 65 P2 P2 C2 C3 C2 50 62 C3 58 62 Demand 120,000 18,000 150,000 10,000 9,300 Selling Price C1 P1 P2 50 46 P2 0