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.

Let

$D_j=$ annual demand for item $j$

$C_j=$ unit cost $of$ item $j$

$s_j=cost$ per order placed for item $j$

$W_j=$ space required for item $j$

$W=$ the maximum amount $of$ space available for all goods

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

The decision variables are $Q_{j^{\text{'}}}$ the amount $of$ item $jto$ order. The model $is$

Minimize ${\displaystyle \underset{j=1}{\overset{N}{}}}[C_j{D}_j+\frac{s_j{D}_j}{Q_j}+i{C}_j\frac{Q_j}{2}]$

$s.t.{\displaystyle \underset{j=1}{\overset{N}{}}}{w}_j{Q}_{j}w$

$,Q_{j}0.$

Construct and solve a nonlinear optimization model for the following data.

Complete the model.

$Q_{1^{\text{'}}},Q_2,$ and $Q_1$$