Air pollution problem Consider an airshed in which there is one major contributor to air pollution—a cement-manufacturing plant whose annual production capacity is $2,500,000$ barrels of cement. Figures are not available to determine whether the plant has been operating at capacity. Although the kilns are equipped with mechanical collectors for air pollution control, the plant still emits $\color{orange}{2.0\text{ Ib }}$ of dust per barrel of cement produced. There are two types of electrostatic precipitators that can be installed to control dust emission. The four-field type would reduce emissions by $\color{orange}{1.5\text{ Ib }}$ of dust/barrel and would cost $\color{blue}{\$0.14/\text{ barrel to operate}}$. The five-field type would reduce emission by $\color{orange}{1.8\text{ Ib }}$ of dust/barrel and would cost $\color{blue}{\$0.18\text{/barrel to operate}.}$ The $\color{red}{\text{EPA requirements}}$ that particulate emissions be reduced by $\color{red}{\text{ at least } 84\%}$. How many barrels of cement should be produced using each new control process to minimize the cost of controls and still meet the $\color{red}{\text{EPA requirements}}$?
The answer is:
objective function: $$z=0.14x+0.18y$$ constraints: $$x+y\le250000 $$ $$0.18-0.12y \le0 $$ $$1.5x+1.8y\le0.84(2x+2y) $$
My question is: What does the second constraint represent? How did we get it?
That second constraint doesn't look correct. It essentially says $y\ge1.5$, and considering the fact that $x+y\le250000$, it is highly likely that $y$ would have been much larger than this anyway. In regards to the text, it doesn't seem to contribute anywhere.