Redo Problem 48 with the restriction that the next week’s production is set to zero if the inventory exceeds 40 carts.

Problem 48

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

I(k + 1) = P(k) + I(k) - S(k)

Where

P(k) = number of carts produced in week k

I(k) = number of carts in inventory in week k

S(k) = number of carts sold in week k

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(l) = 50

(b) An initial inventory of 30 carts so that I(1) = 30.

Transcribed Image Text:

Week 1 2 3 4 6. 7 8 9 10 Sales 50 55 60 70 70 75 80 80 90 55