A coal-fired power plant processes two types of coal, A and B, to generate steam energy....

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A coal-fired power plant processes two types of coal, A and B, to generate steam energy. The coal is first crushed and then burned to produce steam energy to power steam turbines. The question is in what ratio the coal types A and B must be processed to maximize the production of steam energy given a number of limiting conditions. For example, environmental requirements have been imposed on gas and soot emissions. Soot emission levels may not exceed 12 kg per hour, while the require- ment for gas emission is that the number of particles of sulfur per million particles of gas not exceed 3000. Burning 1 ton of coal type A gives a soot emission level of 0.5 kg per hour, and 1 ton of coal type B gives a soot emission level of 1 kg per hour. Coal type A has the property that for every million particles that are released after combustion, 1800 are sulfur particles, while for coal type B, the number of sulfur particles per million of released particles is 3800. Per ton burned, the coal types A and B emit the same number of particles. The coal is transported by train, and the supply is limited to 20 tons an hour. The capacity of the coal-crushing installation is also limited: the crushing capacity is 16 tons of coal type A per hour if A is the only type of coal and 24 tons of coal type B per hour if B is the only one. Finally, after combustion, 1 ton of coal type A gives 12000 kg of steam energy, and 1 ton of coal type B gives 10 000 kg. Formulate this as an LP problem. A coal-fired power plant processes two types of coal, A and B, to generate steam energy. The coal is first crushed and then burned to produce steam energy to power steam turbines. The question is in what ratio the coal types A and B must be processed to maximize the production of steam energy given a number of limiting conditions. For example, environmental requirements have been imposed on gas and soot emissions. Soot emission levels may not exceed 12 kg per hour, while the require- ment for gas emission is that the number of particles of sulfur per million particles of gas not exceed 3000. Burning 1 ton of coal type A gives a soot emission level of 0.5 kg per hour, and 1 ton of coal type B gives a soot emission level of 1 kg per hour. Coal type A has the property that for every million particles that are released after combustion, 1800 are sulfur particles, while for coal type B, the number of sulfur particles per million of released particles is 3800. Per ton burned, the coal types A and B emit the same number of particles. The coal is transported by train, and the supply is limited to 20 tons an hour. The capacity of the coal-crushing installation is also limited: the crushing capacity is 16 tons of coal type A per hour if A is the only type of coal and 24 tons of coal type B per hour if B is the only one. Finally, after combustion, 1 ton of coal type A gives 12000 kg of steam energy, and 1 ton of coal type B gives 10 000 kg. Formulate this as an LP problem.