Optimization $$ Minimizing and Maximizing a FunctionBold text End

In Unit $4,$ we explored examples of how functions are maximized or minimized. Optimization is a powerful calculus tool for finding the $$best way$$ to accomplish a goal. For example:

minimize costs and maximize profit

minimize the distance travelled or maximize the total area of a property

Research and create an authentic optimization$-$type problem not encountered in this course. Be sure to include the following:

A detailed description of what is being maximized or minimized

A full explanation for the reason$($s$)$ why we are maximizing or minimizing a function

The equation of the function being maximized or minimized along with an explanation of how changes in one quantity affect another

A clear description of the variables and algebraic expressions including the use of the proper units of measure

A full solution to the problem while incorporating the use of proper mathematical notation $($Use the five steps found in the beginning of the Action section in Learning Activity $4\mathrm{.}1$ to assist you.$)$