King City Inc. manufactures machine tools. The production planner who oversees the production of two of King City's machines needs to determine exactly how many of each to produce this month. The two machines, TopLathe and BigPress, each require a certain common component. Each TopLathe requires $10$ of these components and each BigPress requires $7.$ Only $56$ components are available this month. The sales department requires that the total number of machines produced in a month must be at least $5($the number TopLathes plus the number BigPresses must be at least $5).$ All machines started in the month must be completed so there are no partially complete machines. The profit for a TopLathe is $$50,000$ and $$34,000$ for a BigPress. Use the attached file, update the Available Components and add any required constraints to determine the optimal profit and the optimal number of TopLathes and BigPresses?

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Profit

TopLathes

BigPresses