Recently chemical engineers have become involved in the area knows 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 X and 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 tone 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 $2000, –$75, and $250/tonne for Z1, Z2 and Z3, respectively. Note that producing Z2 actually creates a loss. The treatment process costs $300/tonne. In addition, the company has access to a limit of 7500 and 12,500 tonnes of X and Y, respectively, during the production period. Determine how much of the products and waste must be created in other to maximize profit.