Philadelphia fun cycles (PFC) manufactures bicycles. All data required to create an aggregate plan including demand for the next year are given below. PFC want's to end the year with an inventory of 1000 bicycles. Assume that PFC's factory is open 20 days each month for 8 hours each day. December's ending inventory Number of workers in December Stockout cost Inventory holding cost 1300 units 90 $50 per unit Month Demand Jan Feb May 1 2 3 4 5 5 3 8 3838 1400 1200 1600 Apr 1500 Hiring workers 1900 Laying off workers 1300 1500 Aug 1200 Sep 2200 Oct 1600 Subcontracting cost Material cost Labour hours required Regular time cost Overtime $10 per unit $400 per worker $800 per worker $140 per unit $75 per unit 10 per unit $30 per hour $15 extra per hour Nov Dec 1400 1500 PFC is considering promoting sales of their bicycles either in February or in September. PFC will drop the sales price of the bicycle from $200 to $190 during the month of promotion. The expected outcome of this action is that PFC will see the consumption in the month increase by 40% (not including forward buying) and a forward buying of 10% from each of the two subsequent months 1. What is PFC's production plan for the coming year without any sales promotions? What the expected total profit? 2. If we promote in February what is the production plan? What is expected total profit? 3. If we promote in September what is the production plan? What is expected total profit? 4. Should PFC go through with sales promotions? If yes, in which month should PFC promote sales?