Consider the following information and answer all the questions asked. Duck-Lovers Unlimited (DLU), assembles specially configured jet aircrafts for airborne duck hunting. The quarterly demand forecasts for the next fiscal year are: Quarter: 1 2 3 4 Demand (units): 10 16 8 14 It takes an average of 2,500 labor hours to assemble each of these aircrafts. Currently, 48 production workers are employed by DLU, working a single 8-hour shift each day. There is no inventory of completed or semi-finished product. In the event of insufficient capacity, demand backlogging is possible, for which a backorder cost of $10,000 per quarter is assessed for each backlogged unit (aircraft). Company policy does not allow lost sales to occur. Labor underutilization or overtime work may be resorted to, but the latter is restricted to no more than 2 hours per shift for each worker. The average regular-time wage rate is $16 per hour, with 50% additional wages for overtime work. These airplanes are sold to an exclusive class of customers for $150,000 each. Material and allocated variable overhead costs amount to $40,000 per unit and inventory holding cost for this product is $4,000/unit/quarter. The workforce size can be varied by hires or layoffs at costs of $1,800 or $1,600 per worker, respectively. On the average, each quarter consists of 500 regular-time hours. (a) Develop (in the tabular form shown below) a quarterly aggregate sales & operations plan (SOP) for DLU, such that a constant and minimum possible workforce size is employed throughout the year (after initial hires or layoffs, as necessary), allowing no overtime, lost sales, backorders or part-time workers. Compute the resulting operating profit for DLU. Demand Reg. Production End. Inventory Workforce Quarter (units) (units) (units) (# of workers) #Hired #Laid Off 1 10 2 16 3 8 4 14 (b) Suppose that no more than 60 production workers can be employed by DLU at any time. Removing all restrictions and requirements stated in part (a), formulate a linear programming model (i.e. clearly and precisely define all variables used, then construct the objective function and all constraints in algebraic format) for determining DLUs optimal 4-quarter SOP. (c) Solve your model in part (b) using Excel/Solver, outlining the plan details.

Consider the following information and answer all the questions asked. Duck-Lovers Unlimited (DLU), assembles specially configured jet aircrafts for airborne duck hunting. The quarterly demand forecasts for the next fiscal year are: It takes an average of 2,500 labor hours to assemble each of these aircrafts. Currently, 48 production workers are employed by DLU, working a single 8-hour shift each day. There is no inventory of completed or semi-finished product. In the event of insufficient capacity, demand backlogging is possible, for which a backorder cost of $10,000 per quarter is assessed for each backlogged unit (aircraft). Company policy does not allow lost sales to occur. Labor underutilization or overtime work may be resorted to, but the latter is restricted to no more than 2 hours per shift for each worker. The average regular-time wage rate is $16 per hour, with 50% additional wages for overtime work. These airplanes are sold to an exclusive class of customers for $150,000 each. Material and allocated variable overhead costs amount to $40,000 per unit and inventory holding cost for this product is $4,000/ unit/quarter. The workforce size can be varied by hires or layoffs at costs of $1,800 or $1,600 per worker, respectively. On the average, each quarter consists of 500 regular-time hours. (a) Develop (in the tabular form shown below) a quarterly aggregate sales \& operations plan (SOP) for DLU, such that a constant and minimum possible workforce size is employed throughout the year (after initial hires or layoffs, as necessary), allowing no overtime, lost sales, backorders or part-time workers. Compute the resulting operating profit for DLU. Q (b) Suppose that no more than 60 production workers can be employed by DLU at any time. Removing all restrictions and requirements stated in part (a), formulate a linear programming model (i.e. clearly and precisely define all variables used, then construct the objective function