Problem $8-14($Algo$)$

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

The monthly forecasts for Product X for January, February, and March are $900,1,550,$ and $1,170,$ 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 $600$ units.

Manufacturing cost is $$210$ per unit, storage cost is $$4$ per unit per month $($based on expected end$-$of$-$month levels$),$ standard pay rate is $$7$ per hour, overtime rate is $$11$ per hour, cost of stock$-$out is $$8$ per unit per month, marginal cost of subcontracting is $$12$ per unit, hiring and training cost is $$120$ per worker, layoff cost is $$220$ per worker, and worker productivity is $0\mathrm{.}1$ unit per hour. Assume that you start off with $40$ workers and that they work $8$ hours per day.

Note: Leave the cells blank, whenever zero $(0)$ is required. Input all values as positive values. Round up $$Workers required$$ to the next higher whole number. Round all other answers to the nearest whole number.