4. (Aggregate Planning) One plant of a company assembles a model of a laser printer. Standards indicate that one worker can assemble five printers per day. This model of the laser printer costs about $350 to make, and the company figures it costs $5 to hold one printer in inventory for one month. Currently, there are 30 printers in inventory, and the inventory level at the end of December is planned to be 50 units. If a printer is backordered, the cost is $35 per unit per month. Currently, there are 9 workers. New workers can be hired at a cost of $500 per worker, and existing workers can be laid off at a cost of $750 per worker. Workers are paid $1500 per month. E (a) Formulate a linear (or an integer, if needed) programming model to obtain an aggregate production plan for the months July through December. Clearly, define the indices, parameters, and decision variables, and write the model with its objective function and constraints. (b) Using GAMS, develop an optimal production plan for the model developed in part (a). Using the optimal solution, for each month tabulate the number of units of product produced, the number of units of product kept in inventory, the number of workers employed, the number of workers hired, and the number of workers fired. (c) Suppose that you are not allowed to change the workforce size. Using the transportation tableau method of developing a production plan, apply the North-West Corner rule to obtain a feasible solution. Using this solution, for each month tabulate the number of units of product produced, the number of units of product kept in inventory, the number of workers employed, the number of workers hired, and the number of workers fired. What is the total cost of production, total cost of inventory holding, total cost of backordering, and total cost of workers