$4.$ Controlling Air Pollution $(15$ Pts$)-$ Nori & Leets Co$.$ is one of the major producers of steel in its part of the world. It is located in the city of Steeltown and is the only large employer there. Steel$$town has grown and prospered along with the company which now employs nearly $50,000$ residents. Therefore, the attitude of the townspeople always has been "What's good for Nori & Leets is good for the town." However, this attitude is now changing; uncontrolled air pollution from the company's furnaces is ruin$$ing the appearance of the city and endangering the health of its residents. A recent stockholders' revolt resulted in the election of a new en$$lightened board of directors for the company. These directors are determined to follow socially responsible policies, and they have been discussing with Steeltown city officials and citizens' groups what to do about the air pollution problem. Together they have worked out stringent air quality standards for the Steeltown airshed. The three main types of pollutants in this airshed are particu$$late matter, sulfur oxides, and hydrocarbons. The new standards require that the company reduce its annual emission of these pol$$lutants by the amounts shown in the following table:

Pollutant Required Reduction in Annual Emission Rate $($in million pounds$)$

Particles $60$

Sulfur Oxides $150$

Hydrocarbons $125$

The board of directors has instructed management to have the engineering staff determine how to achieve these reductions in the most economical way. The steelworks have two primary sources of pollution, namely, the blast furnaces for making pig iron and the open$-$hearth furnaces for changing iron into steel. In both cases, the engineers have decided that the most effective abatement meth$$ods are $(1)$ increasing the height of the smokestacks, $(2)$ using filtler devices $($including gas traps$)$ in the smokestacks, and $(3)$ including cleaner, high$-$grade materials among the fuels for the furnaces. Each of these methods has a technological limit on how heavily it can be used $($e$.$g$.,$ a maximum feasible increase in the height of the smokestacks$),$ but there also is considerable flexibility for using the method at a fraction of its technological limit$.$ The next table shows how much emissions $($in millions of pounds per year$)$ can be eliminated from each type of furnace by fully using any abatement method to its technological limit$.$ Pollutant Taller Smokestacks Filters Better Fuels

Blast

Furnaces Open$-$Hearth

Furnaces

Blast

Furnaces Open$-$Hearth

Furnaces

Blast

Furnaces Open$-$Hearth

Furnaces

Particles $12925201713$

Sulfur Oxide $354218315649$

Hydrocarbons $375328242920$

For purposes of analysis, it is assumed that each method also can be less fully used to achieve any fraction of the abatement ca$$pacities shown in this table. Furthermore, the fractions can be dif$$ferent for blast furnaces and open$-$hearth furnaces. For either type of furnace, the emission reduction achieved by each method is not substantially affected by whether or not the other methods also are used. After these data were developed, it became clear that no single method by itself could achieve all the required reductions. On the other hand, combining all three methods at full capacity on both types of furnaces $($which would be prohibitively expensive if the company's products are to remain competitively priced$)$ is much more than adequate. Therefore, the engineers concluded that they would have to use some combination of the methods, perhaps with fractional capacities, based on their relative costs. Furthermore, be$$cause of the differences between the blast and the open$-$hearth fur$$naces$,$ the two types probably should not use the same combination. An analysis was conducted to estimate the total annual cost that would be incurred by each abatement method. A method's an$$nual cost includes increased operating and maintenance expenses, as well as reduced revenue due to any loss in the efficiency of the production process caused by using the method. The other major cost is the start$-$up cost $($the initial capital outlay$)$ required to in$$stall the method. To make this one$-$time cost commensurable with the ongoing annual costs, the time value of money was used to cal$$culate the annual expenditure that would be equivalent in value to this start$-$up cost$.$ This analysis led to the total annual cost estimates given in the following table for using the methods at their full abatement capacities.

Total Annual Cost from the Maximum Feasible Use of an Abatement