The following information is provided about a furniture factory: Aggregate planning is usually done in terms of direct labor hours. Each of the rm's workers can provide 200 hours of regular-time direct labor per month for a salary of $2000 per month. Overtime is limited to 50 hours per worker per month, at a cost of $15 per hour. The factory currently employs two workers, and can hire additional workers for an estimated $1000 hiring expense per worker. Layos are estimated to cost $500 per worker. Inventory is considered to cost $5 per hour's worth of material carried over per month, while back orders are assumed to cost $25 per hour's worth of demand not met each month (both inventory and back order charges are based on the ending balance for each month). Beginning inventory is zero. Subcontracting is unlimited at a cost of $20 per hour. Expected demand over the next 6 months, in terms of total hours required each month, is as follows: Month 1 2 3 4 5 6 7 8 9 10 Demand 200 600 200 1000 1000 200 200 800 800 1000 (a) Given a constant workforce (no overtime or subcontracting) and the production rate required by the situation just described: How many workers would be needed each month to just satisfy demand over the next 6 months (i.e., ending inventory in month 10 = 0)? Hint: Use the average monthly demand to determine the constant workforce size. Prepare the appropriate aggregate plan using the following table. What would be the cost of this plan? Month 1 2 3 4 5 6 7 8 9 10 Demand 200 600 200 1000 1000 200 200 800 800 1000 RT Production Ending Inventory Inventory Cost (b) What would be the total cost over the next 10 months of hiring and ring as needed in order to use only regular time and avoid overtime, subcontracting, and inventory or back-order costs? Answer the question lling out the following table. Month 1 2 3 4 5 6 7 8 9 10 Demand 200 600 200 1000 1000 200 200 800 800 1000 RT Production Workforce Size Hiring/Firing Cost