Consider a twelve-month sales and operations planning problem with the monthly demand data shown in the table below. Suppose that the inventory holding cost is $20 for each unit held at the end of a month. Each employee makes 10 units per month and each hire costs $200 and each layoff (firing) costs $100. Every plan must start and end with 5 employees. Every plan must start with 20 units of inventory (at the beginning of August).

Month= Aug Sep. Oct Nov. Dec Jan Feb Mar April May June July

Demand (units) = 60 80 60 100 120 40 40 50 60 60 70 60

# Hired =

# Fired =

Inventory =

a) Find the lowest total cost level plan where hiring is allowed only at the beginning of August and firing is allowed only at the end of July. Hiring and firing must be an integer (no fractional hiring/firing). Backordering (negative inventory) is not allowed. For this plan, you do not need to end with 20 units of inventory. (You can end with any non-negative amount of inventory.) Fill in the table above with the number of employees hired and fired at the beginning of each month and the inventory at the end of each month.

# hired in August = _______

# fired at end of July = _______

Inventory at end of July = _______

Total cost for the plan = ___________

b) Find the lowest cost plan where all hiring and firing must be in integers (no fractions) and hiring/firing is allowed in any month. Back ordering (negative inventory) is not allowed. Your plan must end with 20 units of inventory at the end of July. Clearly indicate the number of employees hired and fired at the beginning of each month and the inventory at the end of each month in the table below. Hiring and firing:

Month = August Sep Oct Nov Dec Jan Feb Mar Apr May June July

# Hired =

# Fired =

Inventory =

Total cost for the plan = ___________

c) Suppose your plan must end with 20 units of inventory at the end of July, back ordering (negative inventory) is not allowed, and integer hiring and firing is required. If the inventory holding cost is much less than the $20 used above, briefly describe how the lowest cost plan for hiring and firing in this case would differ from the plans in part a) and in part b) and why these changes are logical.