The forecast demand for aggregate units of chairs in the next three quarters is: Q1: 8900, Q2: 9700, and Q3: 8600. There are currently 30 permanent workers. Each worker can make 300 chairs per quarter. The regular production cost is $20 per chair. The holding cost per unit per quarter is $2, and the backorder cost per unit per quarter is $8. The manager wants to keep a minimum of 30 workers at all times, and he has the option to hire any number of workers for the hiring cost of $1200 per worker. Assuming that the newly hired worker will be laid off by the end of the third quarter (at the latest), the layoff cost will be $600 per worker. Overtime by full-time workers is possible at $25 per unit up to a maximum of 20 percent of regular time production. Current inventory level is zero, but the manager wants to have at least 400 units in inventory at the end of the third quarter. Find the aggregate production plan that minimizes total cost. Assume that when a worker is hired, they will produce exactly equal to the maximum capacity that they have (i.e. 300 units per worker per quarter).