Linear Programming A coal-fired electric plant burns three types of coal to driv

Question

Linear Programming

A coal-fired electric plant burns three types of coal to drive steam turbines in order to produce electricity. Federal standards require that emissions from the furnace stack contain no more than 2500 parts per million (ppm) of sulfur oxide and that no more than 15 kilograms per hour (kg/hr) of particulate matter (smoke) be emitted from the stack. The following table gives the amounts of both pollutants that result from burning the three types of coal. Burning coal A results in 22,000 lb of steam per hour, whereas burning coal B or C, respectively, produces 26,000 or 32,000 lb per hour. The furnace has a capacity for burning 25 tons per hour of any mixture of the three coals. Also, the sulfur oxide emissions that result from burning a mixture of coals is equal to a weighted average of the parts-per-million emissions of the individual coals, where each weight is equal to the proportion of that coal used in the mixture. Formulate a linear programming model for operating the electric plant so as to maximize the amount of steam generated per hour.

Explanation / Answer

Let XA,XB and XC be the number of units burnt of Coal type A, B and C.

We have to maximize the amount of steam generated per hour. Therefore, Objective function would be:

Objective function

Maximize Steam = 22000XA +26000XB +32000XC

We have the following constraints:

XA+XB+XC <=25

2. Emission of sulphur di oxide no more than 15 Kg per hour

XA + 3XB +2XC <=15

3.Sulphur oxide emission is less than or equal to weighted average of parts per million per million of individual coals

12XA +24XB +37XC <= 25(XA+XB+XC)

4.Non negativity constraint

XA,XB,XC>=0

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