Demands for the next six months are 3000, 3200, 4000, 3600, 4200 and 3800. Workforce levels in your factory are fixed and cannot be changed over these six months. Regular time production capacity is 3600 units and overtime production capacity is 400 units every month, with regular time production costing $30 per unit and overtime production costing $45 per unit. Subcontracting to an outside factory can be done at a cost of $50 per unit and has no capacity restrictions, i. e., any number of units can be procured from an outside factory. Costs of holding one unit of inventory for one month is $5. a) If backorders are not allowed, find the aggregate production plan and corresponding cost using the transportation (north-west corner) method. (45 points) b) Assume that backorders are now allowed and cost $10 per unit per month backordered. Find the aggregate production plan and corresponding cost using the transportation (north-west corner) method. c) Can allowing backorders result in a higher total cost of aggregate planning? Briefly explain why r why not.