Reposting this. Previous tutor did not answer all parts of the question. Can you please answer all parts A, B, C, D, E fully. Thank you!

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?(?) = 100 + 30cos(t/6), wheretis in hours since midnight andf(t) represents thousands of gallons of water. The amount of treated water at any given time,t, can be modeled by?(?) = 30?^cos?(?/2).

a) Define a new function,??(?), that would represent the amount of untreated water inside the plant, at any given time,t.

b) Find??(?).

c) Determine the critical values of this function over the interval [0, 24).

d) Determine whether the critical values represent local maximums or minimums.

e) Determine the maximum and minimum amount of untreated water in the plant for the day.

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 amountof untreated water coming into the plant can be modeled byf(t) = 100 + 30cos 2,, where t is in hours since midnight and lit) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 3096059\"). a) Dene a new function, A'(t), that would represent the amount of untreated water inside the plant, at any given time, t. b) Find A'(t). c) Determine the critical values of this function over the interval [0, 24}. d) Determine whether the critical values represent local maximums or minimums. 9) Determine the maximum and minimum amount of untreated water in the plant for the day