Management Science Linear Programing

Dragonball Z Mines Corporation (DZMC) operates strip coal-mining operation in southern Cebu province. Three mine sites (A, B, and C) currently are used, each producing coal of somewhat different sulfur and ash content. Coal from these sites is transported to a common crusher that grinds the coal into a finer mix. The coal is then” washed” to remove some of the sulfur and ash. In the washing process, the crushed coal is fed into a large tank containing a fluid. The cleaner coal floats and is removed for sale. Coal containing a heavier concentration of impurities sinks to the bottom and is discarded.
By using fluids of different densities (that is, having different specific gravities), the amount of impurities removed can be controlled. Three fluids are currently in use, called here Light, Medium, and Heavy. With the Heavy fluid, a greater percentage of the coal is recovered (i.e., floats), but a smaller percentage of impurities is removed. Refer to the Table 1 below.
For example, if the coal from mine A is washed using Light fluid, only 40 percent of the coal is recovered for sale. This recovered coal contains 0.62 percent sulfur and 1.6 percent ash. On the other hand, the use of Heavy fluid increases the yield to 55 percent, but the recovered coal contains 1.04 percent sulfur and 2.1 percent ash. 
The crushing and washing operation is set up so that any combination of coal from the mines can be used in conjunction with any of the fluids. After the washing operation, all the recovered coal is mixed to make one blend, sold by DZMC. Environmental requirements limit the blend to a maximum of 0.5