Consider a twelve-month sales and operations planning problem with the monthly demand data shown in the table below.

- The inventory holding cost is $20 for each unit held at the end of a month.

- Each employee makes 10 units per month.

- Each hire costs $200 and each layoff (firing) costs $100.

- The plan must start and end with 9 employees.

- The plan must start with 40 units of inventory (at the beginning of August).

- The plan must end with at least 40 units of inventory at the end of July.

- Backordering (negative inventory) is not allowed.

Find the lowest cost S&OP plan where all hiring and firing must be in integers (no fractions).

Report the total cost of your plan in part (a), and fill in the table below in part

(b) to show the number of employees hired and fired at the beginning of each month, the production each month and the inventory at the end of each month.

a) Total cost for the plan = _________

b) Fill in the table:

Month	Demand (units)	# Hired	# Fired	Production	Inventory
August	50
September	70
October	80
November	96
December	104
January	90
February	70
March	42
April	58
May	60
June	56
July	64