The economic order quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs included in the model are holding cost per unit, ordering cost, and the cost of goods ordered. The assumptions for that model are that only a single item is considered, that the entire quantity ordered arrives at one time, that the demand for the item is constant over time, and that no shortages are allowed.

Suppose we relax the first assumption and allow for multiple items that are independent except for a restriction on the amount of space available to store the products. The following model describes this situation:

Let

D_j = annual demand for item j

C_j = unit cost of item j

S_j = cost per order placed for item j

i = inventory carrying charge as a percentage of the cost per unit

w_j = space required for item j

W = the maximum amount of space available for all goods

N = number of items

The decision variables are Q_j, the amount of item j to order. The model is:

Minimize
s.t.
	;

In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (D_j/Q_j is the number of orders), and the last term is the annual inventory holding cost (Q_j/2 is the average amount of the inventory).

Set up and solve a nonlinear optimization model for the following data. Enter "0" if your answer is zero.

	Item 1	Item 2	Item 3
Annual Demand	2,100	2,100	1,100
Item Cost ($)	110	60	90
Order Cost ($)	160	140	130
Space Required (sq. feet)	55	30	45
W = 5,300
i = 0.25

Min

+

+

+

+

+

+

s.t
	fill in the blank 8 Q1	+	fill in the blank 9 Q2	+	fill in the blank 10 Q3			fill in the blank 12
					Q1
					Q2
					Q3

If required, round your answer to three decimals.

Q₁ = _______

Q₂ = _______

Q₃ = _______

If required, round your answer to the nearest dollar.

Total Cost = $ _______