DONT USE EXCEL detailed solution !!!!!!!1

(25 points) Suppose that we have 10 bags, and in each bag, there are some items with different colors (A, B, C, D, E represent the items with the corresponding colors) as given in the following table. For example, in bag 3, there are 3 items such that one item of color A, one item of color and one item of color D. We will choose some of these bags such that it will be guaranteed that we have at least 2 items of each color. Moreover, we want to do this by choosing minimum number of bags. Write an integer programming model which will determine which bags should be chosen under the following additional constraints: a. Either bag 1 or bag 8 will be chosen but not both. b. If five or more bags are chosen, than bag 4 must be one of the chosen bags. c. The total number of items in the chosen bags cannot be more than 18. Items in Bags the bag 1 A, B, C A, B, D, E A,C,D CE A, B, C, E A, D, E A,B,C,D A, E B, C, E A, CE 2 3 4 5 6 7 8 9 10 PS. Do not forget to define your decision variables explicitly. (25 points) Suppose that we have 10 bags, and in each bag, there are some items with different colors (A, B, C, D, E represent the items with the corresponding colors) as given in the following table. For example, in bag 3, there are 3 items such that one item of color A, one item of color and one item of color D. We will choose some of these bags such that it will be guaranteed that we have at least 2 items of each color. Moreover, we want to do this by choosing minimum number of bags. Write an integer programming model which will determine which bags should be chosen under the following additional constraints: a. Either bag 1 or bag 8 will be chosen but not both. b. If five or more bags are chosen, than bag 4 must be one of the chosen bags. c. The total number of items in the chosen bags cannot be more than 18. Items in Bags the bag 1 A, B, C A, B, D, E A,C,D CE A, B, C, E A, D, E A,B,C,D A, E B, C, E A, CE 2 3 4 5 6 7 8 9 10 PS. Do not forget to define your decision variables explicitly