A chemicals company produces Sodium based chemicals. The company must plan the workforce levels for the next 5 months. Below table shows the number of workdays and chemical demand (in tons) for each month. The company has 50 workers currently. Each worker can produce 0.2 tons per day.

Table 1: Number of workdays and demand information

Month	Number of Workdays	Demand
1	22	200
2	16	300
3	21	80
4	19	350
5	23	100

The company incurs a hiring cost of $800 and firing cost of $1000 per worker. The payroll is $70

per worker per day. The inventory holding cost for a ton of chemicals for a month is calculated as $5. And the backorder cost for a ton of chemicals per months is calculated as $10.

a. Determine the production plan when the company works with the current number of employees (50 workers). Assume the number of workers will not change during this planning horizon. Calculate the cost of this plan including inventory holding, backorder, and payroll costs.

b. Determine the minimum number of workers that would satisfy the entire demand when backorder is allowed and not allowed. (You need to find two different numbers.) Compare the costs of plans in each case and comment on which plan is better.