Proficiency Assignment: Operating Expenses

Topic: Dynamic Programming.

Suppose you are running a business and you have clients both in Menomonie and in San Francisco. It's a small business with some moveable equipment, so you can run your business out of either city each month. You know how much it would cost to run your business out of each city on any given month, and you know how much it would cost to move the equipment and change which city you're running out of$.$

In other words, you are given $\backslash ($ S$\_\{-\}$ i $\backslash )$ and $\backslash ($ M$\_\{-\}$ i $\backslash )$ for every month $\backslash ($ i $\backslash ),$ and you're given a fixed cost $\backslash ($ X $\backslash )$ which you incur each time you switch locations.

Design a dynamic programming algorithm to find the minimum cost to run your business for an entire sequence of N months.

You will submit a single file containing:

$-$ Your Bellman Equation

$-$ A description of your matrix of subproblem solutions

$-$ Where is the answer within your matrix?

$-$ Your example matrix with all cells filled out