SummerFun, Inc., produces a variety of recreation and leisure products. The production manager has developed an aggregate forecast:

Month	Mar	Apr	May	Jun	Jul	Aug	Sep	Total
Forecast	50	44	55	60	50	40	51	350

Use the following information to develop aggregate plans.

Regular production cost	$	80	per unit	Back-order cost	$	20	per unit
Overtime production cost	$	120	per unit	Beginning inventory		0	units
Regular capacity		40	units per month
Overtime capacity		8	units per month
Subcontracting cost	$	140	per unit
Subcontracting capacity		12	units per month
Holding cost	$	10	per unit per month

b. Develop aggregate plan using the same strategy used in part a except that backlogs are allowed here. There should be no backlog remaining at the end of September. Hint: Use a maximum backlog of 5 in any given month. You will need to develop a set of rules regarding which capacity option (regular, overtime, subcontracting) is always preferable, and regarding the timing of these options (i.e., is it cost-effective to build ahead (and thus carry inventory) or to incur a backlog?). (