CASE $3\mathrm{.}1$ Reclaiming Solid Wastes The Save$-$It Company operates a reclamation center that collects four types of solid waste materials and treats them so that they can be amalgamated into a salable product. $($Treating and amalgamating are separate processes.$)$ Three different grades of this product can be made $($see the first column of the first table below$),$ depending upon the mix of the materials used. Although there is some flexibility in the mix for each grade, quality standards may specify the minimum or maximum amount allowed for the proportion of a material in the product grade. $($This proportion is the weight of the material expressed as a percentage of the total weight for the product grade.$)$ For each of the two higher grades, a fixed percentage is specified for one of the materials. These specifications are given in the following table, along with the cost of amalgamation and the selling price for each grade.