~Optimization problems (also known as max-min problems) have a wide variety of applications in many different fields.

~Among the most popular are those in science & engineering.

~Here is a brief list of certain qualities we seek in these fields. This list is, by no means, complete.

1)  Constructing the largest box with given dimensions (maximizing volume)

2)  Using the least amount of material in constructing a figure that covers a fixed surface area. (minimizing amount of usable material)  

3)  Finding the largest 2-D geometric figure having certain properties. (maximizing area)

4)  Finding the shortest path (minimizing distance) or path of least time (minimizing time)

5)  Finding smallest length or perimeter that encloses a given area. (minimizing length)

6)  Constructing an object that weighs the least. (minimizing weight)

7)  Constructing the strongest object. (maximizing strength)

8)  Finding the fastest velocity or speed. (maximizing speed or velocity)

9)  Finding the quickest reaction time in chemistry. (maximizing reaction rate)

~In business & economics, we are concerned mainly with Maximizing Profit & Minimizing Costs.

~Note:  In all of the above, we need mathematical models (mathematical formulations) that we can use to apply the calculus of optimization analysis to these problems. Some may be very good (laws of physics) & others just good approximations (usually in nonscientific areas).