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Question 2 [25 Marks) A manufacturing facility produces 5 products. Production scheduling is done on an hourly basis. Demand for the products for the next hour is shown below in the column labelled Required Production. The last column shows the production rate for the products in the production cells. Note that the rates are the same for all cells capable of producing a given product. Product 1 2 3 4 5 Required Production 12 17 18 15 8 Production Rate/Hour 10 8 12 10 6 u The facility has 10 cells, each capable of producing some subset of the products. The table below shows cell capability. A blank means that a cell can produce the product while an X indicates that it cannot. 1 2 3 8 10 9 X x 7 X X X Product 1 2 3 4 5 Production Cell 4 5 6 X X X X X X X X X X X X X X X X We want to determine an hourly production schedule that specifies which cells to open and what products should be produced in the open cells. The goal to open as few cells as possible, however, we must open enough cells to make the desired quantities. A cell can produce more than one product type in an hour and the amounts produced do not have to be integer. Construct a model that can be solved for each hour. Solve the problem for the numbers provided in the Required Production column in the first table