MATLAB (Octave) Question

You work at an electronics company that designs and manufactures audio equipment. As an industrial engineer, you oversee (among other things) the production of a line of high end speakers. Your company's current practice is to produce the same number of units as were sold the previous week. The company also has a policy that states that if the inventory ever exceeds the sales of the previous week, the company will only produce half of the number of units as were sold the previous week (in order to ensure that inventory does not get too high). Your boss asks you to do an analysis on the inventory based on projected sales below:

Week: 1 2 3 4 5 6 7 8 9 10

Production: 50 50 55 60 etc.

Sales: 50 55 60 80 70 55 80 80 70 55

Assume that the first week's production is 50 speakers (based on week zero's numbers). Run the program for three cases--a) an initial inventory of 50 speakers and b) an initial inventory of 30 speakers and c) an initial inventory of 10 speakers. Does the inventory ever drop below zero? Should your company change their policy?

To illustrate this example, let's take the case of part a. You have an inventory of 50 speakers, you produce 50 speakers (for a total of 100 speakers), and then you sell 50 speakers. Thus, you are left with 100 - 50 = 50 speakers as your inventory starting off week 2. Then, on week 2, you produce 50 speakers (based on the previous week's sales), giving you a total of 50+50 =100 speakers, and then you sell 55, leaving you with an inventory of 100-55 = 45 speakers at the end of week 2.

Please be as simple as possible complete in full.