DRAGONBALL Z MINES CORPORATION 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 percent sulfur and 2.0 percent ash. Table 1: Effects of Different Fluids on Coal Recovery and Impurities Remaining :1 : Tons of Coal Percent Sulfur Percent Ash Mine Source and Recovered per Content of Content ofmixed to make one blend, sold by DZMC. Environmental requirements limit the blend to a maximum of 0.5 percent sulfur and 2.0 percent ash. Table 1: Effects of Different Fluids on Coal Recovery and Impurities Remaining751 : Tons of Coal Percent Sulfur Percent Ash Mine Source and Recovered per Content of Content of Fluid Type Ton Input Recovered Coa Recovered Coal Mine A 4 Light 0.40 0.62% 1.6% Medium 0.50 0.91 1.9 Heavy 0.55 1.04 2.1 Mine B Light 0.70 0.22 1.9 Medium 0.90 0.35 2.3 Heavy 0.95 0.47 2.5 Mine C Light 0.62 0.42 1.5 Medium 0.75 0.50 1.8 Heavy 0.82 0.78 2.2There are some other restrictions. The equipment available limits the amount that can be produced in each mine. See Table 2 below. The crusher can handle a maximum of 8,000 tons per week of unwashed coal on regular time, but can be worked overtime up to an additional 4,000 tons. The cost of the crushing operation is Php250 per ton of unwashed coal on regular time and Php375 per ton on overtime. The washing tank can handle up to 6,000 tons of recovered coal on regular time and an additional 3,000 tons on overtime. The cost of washing is Php500 per ton of recovered coal on regular time and Php750 on overtime. Table 2: Costs and Capacities of DZMC Capacity (maximum tons Cost (Php per Mine mined per week) ton mined A 6,000 Php 1250 B 2,300 2250 C 5,000 2000 The variable costs of operating each mine are also shown in Table 2. In addition, it costs Php100 per ton of unwashed coal for Light fluid, Php200 per ton of unwashed coal for Medium fluid, and Php300 per ton of unwashed coal for Heavy fluid. DZMC sells its coal blend for Php5,000 per ton. Formulate as an LP model and solve using any software available. Find the optimal production mix for the company