Question $4$

A warehouse needs to distribute goods to five retail stores using the

services of $6$ shipping companies. Each shipping company submits

bids for delivering goods to each store, indicating the total cost they

charge per week for delivery of goods. Once all bids are received, the

warehouse assigns companies to stores and would have to pay the

bid amounts of the selected companies. The warehouse wants to

determine the optimal assignment of shipping companies to retail

stores to minimize the total transportation cost. Not all shipping

companies bid on all stores, and in those cases, the corresponding

entry in the table is marked by $x.$ Each store wants to work with only

one shipping company, and each company cannot service more than

$3$ stores.

The table in the data file shipws the cost $($in thousand of dollars$)$ per

week of goods delivered from each shipping company to each retail

store. Formulate this problem as a network problem using the

template. Consider supply nodes for companies and demand nodes

for stores.

CLICK HERE TO GET THE TABLE OF BIDS darrIn the formulation of the problem, store $3$ has a NET FLOW of $...$

$($enter as a whole number$)$

In the formulation of the problem, what is the smallest capacity that

can be entered for the arc from company $1$ to store $3?($enter as a

whole number$)$

What is the optimal total cost for the warehouse to ship to all stores?

$($if rounding is needed, round to the nearest dollar$)$