Formulate the mixed-integer programming model (explain each step by step)

A company is planning to launching 3 out of 4 new products. To launch each product requires one-time set-up cost and variable production cost as shown in Table 1, To produce the product consumes certain amount of the same type of resource from 3 possible factories. The last row of this table shows the maximum capacity of the resource each factory has. Up to 2 out of the 3 factories will be used to produce the products. If a factory is used to produce any of the products, a factory operating cost will incur, as shown in the second last row of Table 1. Expected demands for the products are also shown in Table 1. If a product is launched, the production should meet the expected demand

Formulate the problem as a mixed-integer programming model to minimize total cost, including factory operating cost, fixed production cost and variable production cost. Clearly define the variables used in the model. The model should be presented with all given data shown in the formulation.

Do NOT solve the formulated model.

Product 1 Product 2 Product 3 Product 4 Fixed Variable Cost Cost 400 5 500 6 600 8 500 4 Factory Operating Cost Maximum Capacity Table 1: Data for Problem 1 Expected Demand Factory 1 2000 25 4000 18 5500 18 3800 44 4000 3500 Resource Requirement Factory 2 28 20 18 36 2000 2500 Factory 3 32 30 28 28 3000 4500