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 jC$\_($j$)=$ unit cost of item jS$\_($j$)=$ cost per order placed for item ji$=$ inventory carrying charge as a percentage of the cost per unitw$=$ the maximum amoufit of space available for all goodsw$\_($j$)=$ space required for item jThe decision variables are Q$\_($j$),$ the amount of item j to order. The model is:

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

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

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

Set up a spreadsheet model for the following data:

$\backslash$table$[[,$Item $1,$Item $2,$Item $3],[$Annual Demand,$3,000,2,000,1,500],[$Item Cost $($$$),90,50,70],[$Order Cost $($$$),150,135,125],[$Space Required $($sq$.$ feet$),50,25,40]]$

$w=5,000$

$j=0\mathrm{.}3$

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 $=$