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Given a word problem, the following steps need to be followed to find the maximum or minimum value of a certain variable specified in the problem:
#color(red)(1))#, Develop the function representing the relationship between that variable and other variables, i.e. if you are asked to minimize a certain surface area you need to develop the area function (equation).
#color(red)(2))#, Develop a function (equation) for the given constraint such as "The volume has to be 1000 Liters.".
#color(red)(3))#, Find a common variable between the two functions, solve for it from the constraint function, and plug it into the other function.
#color(red)(4))#, Take the derivative of the resulting function, set it equal to zero, and solve for its root(s).
#color(red)(5))#, If you get multiple roots determine which one(s) are the absolute extrema and use them to evaluate the remaining variables.
Having said all that, it would be much easier if you posted an optimization problem and looked at the solution someone posts to see how these steps are followed to arrive at the answer.
