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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

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Chapter 16 Solutions
Numerical Methods for Engineers
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