You have a backpack that can carry at most 15 kg of stuff (following image). There are ten boxes of five types (A, B, C, D, and E), with two boxes of each type. The weights and values of the boxes are given in the figure. You want to select some of these boxes to put in your backpack in order to maximize their total value, but you cannot exceed the backpack’s weight capacity. Additionally, • if a type B box is selected, then no type C box can be selected • at least one box of either type A or type D must be selected Formulate an integer linear programming model to help you make the bag packing decision. To assist you, below are your decision variables. • yi: select (= 1) or not select (= 0) type i box, i = A, B, C, D, E. • xj: The number of type j boxes selected, j = A, B, C, D, E.
You have a backpack that can carry at most 15 kg of stuff (following image). There are ten boxes of five types (A, B, C, D, and E), with two boxes of each type. The weights and values of the boxes are given in the figure. You want to select some of these boxes to put in your backpack in order to maximize their total value, but you cannot exceed the backpack’s weight capacity. Additionally,
• if a type B box is selected, then no type C box can be selected
• at least one box of either type A or type D must be selected
Formulate an integer linear programming model to help you make the bag packing decision.
To assist you, below are your decision variables.
• yi: select (= 1) or not select (= 0) type i box, i = A, B, C, D, E.
• xj: The number of type j boxes selected, j = A, B, C, D, E.
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