The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance
Distribution Center
1 2 3
Plant 1 800 miles 1,100 miles 600 miles
2 1,300 miles 1,400 miles 1,200 miles
3 400 miles 600 miles 800 miles
4 700 miles 1,000 miles 900 miles
The freight cost for each shipment is $100 plus 50 cents per mile.
How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost?
(a) Formulate this problem as a transportation problem by constructing the appropriate parameter table.
(b) Draw the network representation of this problem.