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 $1,020,1,480,$ and $1,180,$ 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 $480$ units.

Manufacturing cost is $$160$ per unit, storage cost is $$6$ per unit per month $($based on expected end$-$of$-$month levels$),$ standard pay rate is $$6$ per hour, overtime rate is $$9$ per hour, cost of stock$-$out is $$8$ per unit per month, marginal cost of subcontracting is $$8$ per unit, hiring and training cost is $$140$ per worker, layoff cost is $$240$ per worker, and worker productivity is $0\mathrm{.}1$ unit per hour. Assume that you start off with $42$ 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.

ForecastSafety stockBeginning inventoryNet production requiredWorkers requiredHired$|$Laid offActual productionEnding inventoryLaborInventoryHiringLayoffTotalJanuaryJanuay$1,020$FebruaryFebruary$1\mathrm{.}480$Total SMarchMarch$1\mathrm{.}180$