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 $j$

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

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

$w_j=$ space required for item $j$

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

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

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

$,Q_{j}0$

$Q_{j}0,j=1,2,$dotsN

Set up a spreadsheet model for the following data:

$W=5,000$

$i=0\mathrm{.}3$

Solve the problem using Excel Solver. Hint: You will need to start with decision variable values that are greater than $0$ for Solver to find a solution.

If required, round your answers to two decimal places.

Optimal Solution:

$Q_1=$

$Q_2=$

$Q_3=$

If required, round your answer to the nearest dollar. Do not round intermediate calculations.

Total cost $=$