Chapter 3.1, Problem 46E

For Exercises 42–47, perform the following steps.

1. (a) Write a system of inequalities to express the conditions of the problem.
2. (b) Graph the feasible region of the system.

46. Production Scheduling A cement manufacturer produces at least 3.2 million barrels of cement annually. He is told by the Environmental Protection Agency (EPA) that his operation emits 2.5 lb of dust for each barrel produced. The EPA has ruled that annual emissions must be reduced to no more than 1.8 million lb. To do this, the manufacturer plans to replace the present dust collectors with two types of electronic precipitators. One type would reduce emissions to 0.5 lb per barrel and operating costs would be 16¢ per barrel. The other would reduce the dust to 0.3 lb per barrel and operating costs would be 20¢ per barrel. The manufacturer does not want to spend more than 0.8 million dollars in operating costs on the precipitators. He needs to know how many barrels he could produce with each type. Let x = the number of barrels (in millions) produced with the first type and y = the number of barrels (in millions) produced with the second type.