Suppose that a manufacturing company builds n different types of robots, say robots 1, 2, . . . , n. These robots are made from a common set of m types of materials, say materials 1, 2, . . . , m. The company has only a limited supply of materials for each year, the amount of materials 1, 2, . . . , m are limited by the numbers b1, b2, . . . , bm, respectively. Building robot i requires an aij amount from material j. For example, building robot 1 requires a11 from material 1, a12 from material 2, etc. Suppose the profit made by selling robot i is pi. Write an integer linear program for maximizing the annual profit for the company

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Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.