The monthly forecasts for the product X for January, February, and March are $1,000,1,500,$ and $1,200,$ 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 $500$ units. Manufacturing cost is $$200$ per unit, storage cost is $$3$ per unit per month $($based on expected end$-$of$-$month levels$),$ standard pay rate is $$18$ per hour, hiring and training cost is $$2,000$ per worker, layoff cost is $$3,000$ per worker, and worker productivity is $0\mathrm{.}1$ unit per hour. Assume that you start off with $50$ workers and that they work $8$ hours per day.