$3.$ Semiconductor Plant $(15$ Pts$)$

You are the General Manager of a US owned plant located in Northern Mexico. The firm manufactures semiconductors and uses temporary employees from the local area to fulfill production labor requirements. Each quarter employees are hired and released depending upon production requirements and needs. The firm has a maximum storage capacity of $1,000,000$ semiconductors. Agreements with the Mexican Government require that at least $325$ workers must be on the payroll each quarter. There are currently $375$ employees on the payroll and $120,000$ semiconductors in storage. Sales forecast provided by the marketing department are estimated as follows for the upcoming year:

PRODUCTION PREDICTED

QUARTER DAYS SALES FORECAST

First $59940,000$

Second $621,215,000$

Third $55860,000$

Fourth $58430,000$

Inventory holding cost are $$\mathrm{.}25$ per semiconductor per quarter. The holding cost applies to excess inventory after demand is fulfilled. Thus, assume inventory produced in the quarter to fulfill demand in that quarter is not subjected to holding cost.

The firm would like to have at least $100,000$ semiconductors in stock at the end of the year. Each employee produces an average of $30$ semiconductors per day. The cost of hiring a new worker is $$200,$ and the cost of releasing a worker is $$400.$ Determine a production plan that minimizes total cost and meets demand forecasts. This production plan must indicate the amount of inventory to produce, store and the amount of workers to hire and release each quarter. Use LP to determine a solution for this problem.