A certain company manufactures and sells golf carts. At the end of each week, the company...

A certain company manufactures and sells golf carts. At the end of each week, the company transfers the carts produced that week into storage (inventory). All carts that are sold are taken from the inventory. A simple model of this process is

where

The projected weekly sales for 10 weeks are

Suppose the weekly production is based on the previous week’s sales so that P(k) = S(k − 1). Assume that the first week’s production is 50 carts; that is, P(1) = 50. Write a MATLAB program to compute and plot the number of carts in inventory for each of the 10 weeks or until the inventory drops below zero. Run the program for two cases: a. an initial inventory of 50 carts so that I(1) = 50, and b. an initial inventory of 30 carts so that I(1) = 30.