Problem $19-14($Algo$)$

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 $1,050,1,450,$ and $1,240,$ 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 $520$ units.

Manufacturing cost is $$2,700$ per unit, storage cost is $$7$ per unit per month $($based on expected end$-$of$-$month levels, standard pay rate is $$21$ per hour, hiring and training cost is $$2,700$ per worker, layoff cost is $$3,700$ per worker, and worker productivity is $0\mathrm{.}1$ unit per hour. Assume that you start off with $41$ workers and that they work $8$ hours per day.

Note: Leave no cells blank $-$ be certain to enter $"$O$"$ wherever required. Input all values as positive values. Round Workers Required up to next higher whole number. Round all other variables to nearest whole number.

$\backslash$table$[[,$January,February,March$],[$Forecast$,1,050,1,450,1,240],[$Safety stock required,,,$],[$Working days,,,$],[$Beginning inventory,,,$],[$Net production required,,,$],[$Hours required,,,$],[$Workers required,,,$],[$Hired$,,,],[$Laid off,,,$],[$Actual production,,,$],[$Ending inventory,,,$]]$

$\backslash$table$[[,$January,February,March$],[$Labor cost$,,,],[$Inventory cost$,,,],[$Hiring cost$,,,],[$Layoff cost$,,,],[$Total cost$,,,],[$Total$,,,]]$