1. Project: Optimizing at a Water-Treatment Plant Imagine you are an engineer for a water-treatment plant, and you must determine the optimal amount of water in the plant over a 24-hour period. On a particular day, the amount of untreated water coming into the plant can be modeled by f (t) = 100 + 30cos 2,, where t is in hours since midnight and t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e\"5