Acme Inc. sources a key component used in its product from ABC Enterprise. Based on Acmes production schedule they require the component in the following quantities over the next 6 months.

	1	2	3	4	5	6
Items Required	1850	1550	1475	1800	1360	1860

ABC ships this component in 3 standard cases with discounts offered on larger cases.

	Items/Case	Unit Cost	Case Cost
Small	50	10.00	500
Medium	100	9.50	950
Large	250	9.00	2250

In addition to the purchase cost ABC incurs a holding cost for the inventory items left over at the end of the month of $10 per unit. The on-hand balance of the item is currently 0. A material planner for ABC is attempting to develop an ordering plan for this item that minimizes total costs.

Complete the descriptive model:

Calculate the number of items ordered by multiplying the number of cases ordered by the case size.

Calculate the purchase cost by multiplying the number of cases ordered by the case cost.

Calculate the carrying cost on inventory by multiplying the ending balance by $10.

Formulate the decision problem as an LP relaxation (i.e. a problem without integer constraints) with the following constraints:

Order quantities are nonnegative.

Monthly ending balance is greater than or equal to 0

Solve the model and report the following:

Average on hand balance

Total # of cases ordered by size (small, medium, large)

Purchase cost, holding cost and total cost

Now apply integrality restrictions by manually rounding the order quantities in each month. Work from month 1 to 6, round down when you can but make sure that a non-negative balance is maintained. (Only round non-zero items.) Report inventory, ordering and cost information from your manual solution.

Now apply integrality constraints on the model and use Solver to solve the integer program. Report inventory, ordering and cost information from your solution.