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In this example, the Pittsburgh Steel Co. has been contracted to produce a new type of steel that has given tight quality requirements. You have a given amount of materials available for mixing up a batch. A one-ton (2000 lb.) batch must be blended that satisfies the quality requirements stated earlier. The problem now is what amounts of each of the eleven materials should be blended together so as to minimize the cost but satisfy the quality requirements. A steel expert claims that the least cost mix will not use any more than nine of the eleven available raw materials. What is a good blend? Most of the eleven prices and four quality control requirements are negotiable. Which prices and requirements are worth negotiating?
Note that the chemical content of a blend is simply the weighted average of the chemical content of its componenets. Thus, for example, if we make a blend of 40 percent Alloy 1 and 60 percent Alloy 2, the manganese content is (0.40)*60+(0.60)*9=29.4.