Suppose your group has just been hired by a company called Alco. You are asked to analyze its operations and make some recommendations about how it can comply at a minimum cost with recent orders of the Environmental Protection Agency (EPA). To prepare your report, you study the operation and obtain the following information:

- Alco Cement Company produces cement.

- The EPA has ordered Alco to reduce the amount of emissions released into the atmosphere during production.

- Alco wants to comply, but wants to do so at the least possible cost.

- Present production is 2.5 million barrels of cement, and 2 pounds of dust are emitted for every barrel of cement produced.

- The cement is produced in kilns that are presently equipped with mechanical collectors.

- To reduce the emissions to the required level, the mechanical collectors must be replaced either by four-field electrostatic precipitators, which would reduce emission to 0.5 pound of dust per barrel of cement, or by five-field precipitators, which would reduce emission to 0.2 pound per barrel.

- The capital and operating costs for the four-field precipitator are \(14 otin\) per barrel of cement produced; for the five-field precipitator, costs are \(18 \phi\) per barrel.

- To comply with the EPA, Alco must reduce particulate emission by at least 4.2 million pounds.