Develop a production schedule to produce the exact production requirements by varying the workforce size for the following problem. Evaluate the cost of production schedule.

The monthly forecasts for the product X for January, February, and March are $930,1,550,$ and $1,220,$ respectively. Safety stock policy recommends that half of the forecast for that month be defined as safety stock. There are $22$ working days in January, $19$ in February, and $21$ in March. Beginning inventory is $550$ units.

Manufacturing cost is $$2,800$ per unit, storage cost is $$6$ per unit per month $($based on expected end$-$of$-$month levels, standard pay rate is $$12$ per hour, hiring and training cost is $$2,800$ per worker, layoff cost is $$3,800$ per worker, and worker productivity is $0\mathrm{.}1$ unit per hour. Assume that you start off with $47$ workers and that they work $8$ hours per day.