Math $1220-$ Project $3$

Optimization

In this project, you will demonstrate your ability to apply the methods of calculus to solve optimization problems. To get a passing grade on this project you must communicate clearly and effectively, using both ordinary English and mathematics.

Problem I A womp rat rancher wants to use some extra fencing material to build an enclosure up against an existing wall. Here is the situation:

there is a grand total of $1000$ meters of fencing material

there is only one corner post, so the enclosure must be built in the shape of a right triangle

there is a fierce prevailing wind that blows along the direction of the existing wall, and the fencing material will need to be doubled up on one side to provide ample protection from the blowing sand.

The following diagram illustrates the situation

This rancher asks you to use your calculus powers to design the new fence so that the new yard will be able to accommodate as many womp rats as possible.

Solve the problem and write up your results with good communication, so that the rancher will

be able to understand your process and have confidence in your conclusions

have clear instructions for building the fence in the best possible way.