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Dont forget to add a constraint that each object can

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Formulate an AMPL model for this situation. Don’t forget to add a constraint that each object can only go into one knapsack! Using the data from 1a, solve for two knapsacks of weight limit 50. How does the solution differ from your previous one? (c) Superficially, the preceding knapsack problem resembles an assignment problem: we have a col- lection of objects and a collection of knapsacks, and we want to make an optimal assignment from members of the former to members of the latter. What is the essential difference between the kinds of assignment problems described in Taha chapter 5 and the knapsack problem described in 1b? (d) Suppose that you can put up to three of each object in the knapsack, instead of just one. Revise the model of 1a to accommodate this possibility, and re-solve with the same data. How does the optimal solution change?
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2. (20 pts) The output of a paper mill consists of standard rolls 110 inches (110”) wide, which are cut into smaller roles to meet orders. This week there are orders for rolls of the following widths: Width Orders 20” 48 45” 35 50” 24 55” 10 75” 8 The owner of the mill wants to know what cutting patterns to apply so as to fill the orders using the smallest number of 110” rolls. A cutting pattern consists of a certain number of rolls of each width, such as two of 45” and one of 20”, or one of 50” and one of 55” (and 5” of waste). Suppose that we consider only the following six patterns: Width 1 2 3 4 5 6 20” 3 1 0 2 1 3 45” 0 2 0 0 0 1 50” 1 0 1 0 0 0 55” 0 0 1 1 0 0 75” 0 0 0 0 1 0 (a) How many rolls should be cut according to each pattern to minimize the number of 110” rolls used? To put it another way, we are given a supply of wide rolls, orders for narrower rolls, and a set of patterns. We seek a combination of patterns that fills all orders using the least amount of material.
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