The company has four distribution centers, located in Atlanta, Lexington, Milwaukee, and Salt Lake City, and ships to 12 retailstores, located in Seattle, San Francisco, Las Vegas, Tucson,Denver, Charlotte, Minneapolis, Fayetteville, Birmingham, Orlando, Cleveland, and Philadelphia. The company wants to minimize the transportation costs of shipping one of its products. The per-unit shipping cost from each distribution center to each retail location and the amounts currently in inventory and ordered at each retail location are shown in the accompanying table. Develop and solve an optimization model to minimize the total transportation cost and answer parts a and b.

a. What is the minimum cost of shipping?

 

A 1 2 Seattle 3 San Francisco 4 Las Vegas 5 Tucson 6 Denver 7 Charlotte B Atlanta C Lexington $1.95 $2.00 $1.70 $1.53 $1.10 $0.55 $0.60 $1.05 $0.60 $0.50 $0.60 $0.25 $0.50 $0.30 41000 $2.15 $2.10 $1.75 $1.50 $1.20 $0.65 8 Minneapolis $0.90 9 Fayetteville. $0.80 10 Birmingham $0.35 11 Orlando $0.15 12 Cleveland 13 Philadelphia 14 Supply 15 16 17 33300 D Milwaukee $1.70 $1.85 $1.50 $1.41 $0.95 $0.40 $0.40 $0.95 $0.70 $0.70 $0.35 $0.40 15700 E Salt Lake City $0.60 $0.55 $0.35 $0.60 $0.40 $0.95 $1.00 $1.10 $1.35 $1.60 $1.60 $1.70 16000 F Demand 5500 16000 4200 3400 5000 7000 3000 9500 3100 13000 10000 14000 G