Chapter 16, Problem 6P

Recently chemical engineers have become involved in the area known as waste minimization. This involves the operation of a chemical plant so that impacts on the environment are minimized. Suppose a refinery develops a product Z1 made from two raw materials Xand Y. The production of 1 metric tonne of the product involves 1 tonne of X and 2.5 tonnes of Y and produces 1 tonne of a liquid waste W. The engineers have come up with three alternative ways to handle the waste:

• Produce a tonne of a secondary product Z2 by adding an additional tonne of X to each tonne of W.

• Produce a tonne of another secondary product Z3 by adding an additional tonne of Y to each tonne of W.

• Treat the waste so that it is permissible to discharge it.

The products yield profits of $\$2500,-50$, and $\$200/\text{tonne}$ for Z1, Z2, and Z3, respectively. Note that producing Z2 actually creates a loss. The treatment process costs $\$300/\text{tonne}$. In addition, the company has access to a limit of 7500 and 10,000 tonnes of X and Y, respectively, during the production period. Determine how much of the products and waste must be created in order to maximize profit.