Optimization of a Water Purification Process

by Christopher Bahamundi

Submitted : Fall 2011

The objective of this project was to find the cycle time for a water purification machine that will maximize the company’s profit, the corresponding profit in $/yr, and the gallons per year of purified water that are produced. In order to meet this objective, I had to formulate an equation for annual profit based on cycle time t, water production rate p, and number of cycles per year n to determine the company’s profit on an annual basis in terms of cycle time t. In order to find the profit of the company on a yearly basis, I had to take the annual sales and subtract it by the annual costs using given constraints to express p and n in terms of t. After finding the equation for profit in terms of cycle time t, I was able to take the derivative of the equation and find the maximum output which is 61.4657 so about 61 ½ days. This result determines the length of the cycle time required in order to maximize the company’s profit on an annual basis. This also shows that the maximum profit generated on an annual basis is $59,441.98, and the number of gallons produced is 40,653.32.

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