A company has 4 production facilities. Each facility is eligible to produce Product A, Product B or Product C, but it can only produce one of these products. The annual fixed cost of operating each...

A company has 4 production facilities. Each facility is eligible to produce Product A, Product B or Product C, but it can only produce one of these products. The annual fixed cost of operating each facility and the variable cost of producing a product of each type at each facility are given in the table.

Facility Fixed Cost ($) Variable Cost ($) Product A Product B Product C Facility 1 8,000,000 1200 1600 900 Facility 2 6,000,000 1500 1800 1100 Facility 3 4,000,000 1700 1900 1200 Facility 4 3,000,000 1900 2200 1400 The company must produce 5000 units of each type of product in a year. Formulate an IP to minimize the total annual production cost satisfying the following constraints:  Each facility can produce only one type of product.  The total production of each type of product must be at a single facility. For instance, if any Products A are produced at facility 1, then all Products A must be produced there.  If facilities 3 and 4 are used, then facility 1 must also be used.