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Question: apec 6300 quantitative analysis for business and policy decisions review...

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APEC 6300: Quantitative Analysis for Business and Policy Decisions Review Questions Part II LP Modeling Revised Janaury 16, 2019 Problem 1. Example in section 1.3. in Bradley, Hax, and Magnanti, pages 5-8): Charging a Blast Furnace An iron foundry has a firm order to produce 1000 pounds of castings containing at least 0.45 percent manganese and between 3.25 percent and 5.50 percent silicon. As these particular castings are a special order, there are no suitable castings on hand. The castings sell for $0.45 per pound. The foundry has three types of pig iron available in essentially unlimited amounts, with the following properties: Type of pig iron % 1% 0.6% Silicon Manganese 045% 0.5% 0.4% Further, the production process is such that pure manganese can also be added directly to the melt. The costs of the various possible inputs are: Pig A Pig B Pig C Manganese $21/thousand pounds $25/thousand pounds $15/thousand pounds S8/pound. It costs 0.5 cents to melt down a pound of pig iron. Out of what inputs should the foundry produce the castings in order to maximize profits?

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