A company uses production capacity at two processing plants, Plants P1 and P2, to complete the...

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A company uses production capacity at two processing plants, Plants P1 and P2, to complete the manufacture of its product. Production takes place in two stages, and the each plant has the ability to engage in both stages of production, as shown in Table 1. From the last column of the table, note that it is possible to ship items that have gotten through Stage 1. production at plant P2 to complete production at plant P1 (subject to its total processing capacity). The goal is to generate a plan that maximizes production for the week. Table 1: Data for the production planning problem Plant P1 P2 1st stage 2nd stage production capacity production capacity (hundreds of units / week) (hundreds of units / week) 4 5 4 2 Shipping capacity (unfinished products from P2 to P1) (hundreds of units / week) N/A 2 Problem 1 1. Formulate a min-cost flow model in standard form whose solution describes the production- maximizing plan. 2. Propose an initial flow of the appropriate value that is not minimum cost. 3. Use cycle-canceling to compute an optimal solution to the min-cost flow model. It is not necessary to show Bellman-Ford calculations, but otherwise be sure to show all steps of the algorithm. A company uses production capacity at two processing plants, Plants P1 and P2, to complete the manufacture of its product. Production takes place in two stages, and the each plant has the ability to engage in both stages of production, as shown in Table 1. From the last column of the table, note that it is possible to ship items that have gotten through Stage 1. production at plant P2 to complete production at plant P1 (subject to its total processing capacity). The goal is to generate a plan that maximizes production for the week. Table 1: Data for the production planning problem Plant P1 P2 1st stage 2nd stage production capacity production capacity (hundreds of units / week) (hundreds of units / week) 4 5 4 2 Shipping capacity (unfinished products from P2 to P1) (hundreds of units / week) N/A 2 Problem 1 1. Formulate a min-cost flow model in standard form whose solution describes the production- maximizing plan. 2. Propose an initial flow of the appropriate value that is not minimum cost. 3. Use cycle-canceling to compute an optimal solution to the min-cost flow model. It is not necessary to show Bellman-Ford calculations, but otherwise be sure to show all steps of the algorithm.

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