ABC Co$.$ is to plan its workforce and production levels for next year. Forecast demands for the next $4$ quarters are $1160,960,1150,1380$ units. Ending inventory of last year is expected to be $60,$ and the ABC would like to have a minimum of $50$ units in inventory at the end of next year. The cost of holding one unit in inventory for one quarter is $$190.$

There are currently $200$ workers. The cost of hiring one worker is $$700,$ and the cost of firing one worker is $$1500.$

In the past, the plant manager observed that over $60$ working days and with the workforce level constant at $200$ workers, ABC produced $1200$ units.

The number of working days for the next $4$ quarters are respectively $61,62,65,$ and $58.$

Assume that ABC plans to adopt a level strategy $($constant workforce plan$)$ for next year.

$($a$)(10$ pts$)$ Determine the level of workforcefor next year such that all quarterly demands will be met. How many workers does ABC need to hire at the beginning of next year?

$($A$)$ Hire $9$ workers

$($B$)$ Hire $2$ workers

$($C$)$ Fire $6$ workers

$($D$)$ Fire $11$ workers

$($b$)(7pts)$ Find the inventory level at the end of next year.

$($A$)52$

$($B$)55$

$($C$)59$

$($D$)64$

$($c$)(8pts)$ Compute the total cost $($including hiring$/$firing cost and inventory cost$)$ under the constant workforce plan for next year.

$($A$)$ $$142600$

$($ii$)$ $$153350$

$($C$)$ $$164420$

$($D$)$ $$175500$

$2(25$ points$).$ Same as Problem $1,$ except that the forecast demands for the next $4$quarters are $1160,1260,1150,980$ units.

$($a$)(15$ pts$)$ Determine the level of workforce for next year such that all quarterly demands will be met $($no backlogging$).$

$($A$)185$ workers

$($B$)189$ workers

$($C$)192$ workers

$($D$)195$ workers