How Do You Approach Modeling and Optimization Problems?

[unf0r5ak3n]

We have just begun this topic and I'm really confused about how to approach questions, is there any trick or guideline for doing so?

Ex: Consider an isosceles right triangle whose hypotenuse is the x-axis and whose vertex is on the y-axis. If the hypotenuse is 2 units long, we'd have x-intercepts of -1 and 1. What is the largest area possible for a rectangle inscribed in the triangle?

 

[hotvette]

The first thing you need to do in this case is draw a picture of the given geometry and label it with known information. Since the goal is to maximize something, a trigger should go off in your head that you'll need to differentiate a function and set it equal to zero. Third, you need to develop an equation of the thing you are trying to optimize (in this case, area of a rectangle) as a function of a single variable (so you'll have something to solve for). That's pretty much it.