ABC Company uses overtime, inventory and subcontracting to
absorb the fluctuations in demand for its playgrounds for children.
An aggregate production plan is devised annually and updated
quarterly. Cost data, expected demand, and available capacities in
units for the next four quarters are given here. Demand must be
satisfied in the periods it occurs; that is, no backordering is
allowed. Design a production plan that will satisfy demand at
minimum cost.          

       Expected  
Regular   Overtime   Subcontract

Quarter   Demand  
Capacity   Capacity   Capacity

   1      
   650   750   100  
500

   2      
   1250   950   150  
500

   3       
   1350   1050   200  
500

   4      
   2750   1050   200  
500

Regular production cost per unit      
    $200

Overtime production cost per unit      
    $250

Subcontracting production cost per unit  
    $300

Inventory holding cost per unit per period  
   $30

Beginning Inventory      
            300
units