A company has hired you to develop an aggregate plan to determine the number of workers they will need for the next 9 months (February through October). This company makes 8 different products. The time (in hours) required to produce each product is as follows:

Product	Number of hours to produce 1 unit
Product A	1.82
Product B	0.86
Product C	2.55
Product D	4.49
Product E	0.89
Product F	3.78
Product G	0.75
Product H	2.29

Suppose the following demands for each product have been forecast for the next 9 months:

Month	# days per month	Forecast Demand
		Product A	Product B	Product C	Product D	Product E	Product F	Product G	Product H
February	22	305	660	636	1858	424	1941	255	441
March	20	383	590	547	1162	432	2009	296	432
April	28	550	1085	980	3220	886	3642	486	802
May	21	328	711	529	1627	388	1864	252	363
June	25	184	424	346	1127	295	1213	153	267
July	27	201	419	417	1345	295	1357	193	285
August	31	417	718	598	2122	500	1919	284	488
September	28	234	601	499	1613	363	1561	224	375
October	31	120	244	186	662	153	630	88	167

When developing aggregate plans the company assumes workers regularly work 8 hours each day; no overtime or subcontracting will be used. The firm would like to maintain a minimum buffer inventory (i.e. safety stock) each month (see table below). The starting inventory level (i.e. inventory at end of January), desired inventory at the end of the planning horizon (in addition to monthly safety stock), initial workforce level, hiring cost, firing cost, regular time cost, and inventory holding cost (in $ per aggregate unit per month) are shown in the table below. Based on the aggregate forecast demand and planning parameters (in table below), determine the number of workers this company will need over the next 9 months using the following aggregate planning strategies.

Safety Stock (in aggregate units)	600
Beginning of planning horizon Inventory (in aggregate units)	1000
End of planning horizon Inventory, additional to any SS (in aggregate units)	0
# workers employed at end of January	100
Hiring Cost (in $ per hired worker)	$1,000
Firing Cost (in $ per fired worker)	$500
Regular Time Cost (in $ per hour)	$45.00
Inventory Holding Cost (in $ per aggregate unit per month)	$7.50

1. Find the minimum constant workforce needed to meet demand assuming no shortages are allowed (i.e. no negative inventory in any month). What is the cost associated with this constant workforce strategy? Note: use scheduled idle time to find the minimum cost solution.

2. Find the number of workers needed each month using the zero inventory strategy (no shortages allowed). What is the cost associated with this zero inventory workforce strategy? Note: use scheduled idle time to find the minimum cost solution.

3. Find the number of workers needed each month using a mixed strategy (no shortages allowed). What is the cost associated with this mixed strategy? Note: use scheduled idle time to find the minimum cost solution.