# solution

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

Dj = annual demand for
item j

Cj = unit cost of
item j

Sj = cost per order placed for
item j

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

wj = space required for
item j

W = the maximum amount of space available for all
goods

N = number of items

The decision variables are Qj, 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
(Dj/Qj is the number
of orders), and the last term is the annual inventory holding cost
(Qj/2 is the average amount of the
inventory).

Set up and solve a nonlinear optimization model for the

 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 Ã— Q1 + fill in the blank 9 Ã— Q2 + fill in the blank 10 Ã— Q3 = fill in the blank 12 Q1 = Q2 = Q3 =

Q1 = _______

Q2 = _______

Q3 = _______