Elray Manufacturing Company produces office supplies but outsources the delivery of its products to third-party carriers. Offhaus ships to 20 cities from its Glassboro, NJ, manufacturing facility and has asked a variety of carriers to bid on its business. Seven carriers have responded with bids. The resulting bids (in dollars per truckload) are shown in the table. For example, the table shows that carrier 1 bid on the business to cities 1120. The right side of the table provides the number of truckloads scheduled for each destination in the next quarter. Bid $/Truckload Demand Carrier 1 Carrier 2 Carrier 3 Carrier 4 Carrier 5 Carrier 6 Carrier 7 Destination (Truckloads) City 1 $2188 $1666 $1790 City 1 City 2 $1453 $2602 $1767 City 2 City 3 $1534 $2283 $1857 $1870 City 3 City 4 $1687 $2617 $1738 City 4 City 5 $1523 $2239 $1771 $1855 City 5 City 6 $1521 $1571 $1545 City 6 City 7 $2100 $1922 $1938 $2050 City 7 City 8 $1800 $1432 $1416 $1739 City 8 City 9 $1134 $1233 $1181 $1150 City 9 City 10 $672 $610 $669 $678 City 10 City 11 $724 $723 $627 $657 $706 City 11 City 12 $766 $766 $721 $682 $733 City 12 29 City 13 $741 $745 $682 $733 City 13 City 14 $815 $800 $828 $745 $832 City 14 City 15 $904 $880 $891 $914 City 15 10 City 16 $958 $933 $891 $914 City 16 10 City 17 $925 $929 $937 $984 City 17 City 18 $892 $869 $822 $829 $864 City 18 25 City 19 $927 $969 $967 $1008 City 20 $963 $938 $955 $995 City 19 City 20 12 10 8024222333=223223322 10 10 10 12 25 25 11 12 Number of Bids 10 10 10 7 20 5 18 Because dealing with too many carriers can be cumbersome, Offhaus would like to limit the number of carriers it uses to three. Also, for customer relationship reasons, Offhaus wants each city to be assigned to only one carrier (that is, there is no splitting of the demand to a given city across carriers). a. Develop a model that will yield the three selected carriers and the city-carrier assignments that minimize the cost of shipping. Model the problem. b. Offhaus is not sure whether three is the correct number of carriers to select. How would you modify the model?