A shipping company ShipCo supplies four destinations (D1,D2,D3,D4) from four sources (S1,S2,S3,S4). The shipping cost (in...

A shipping company ShipCo supplies four destinations (D1,D2,D3,D4) from four sources (S1,S2,S3,S4). The shipping cost (in dollars) per shipment from each source to each destination is given below.

	D1	D2	D3	D4
S1	7	8	5	2
S2	2	9	1	4
S3	4	5	3	1
S4	2	1	4	3

The four sources make 10, 20, 20, and 10 shipments per month, respectively. The four destinations need to receive 20, 10, 10, and 20 shipments per month, respectively. The manager of ShipCo now wants to determine the best plan for how many shipments to send from each source to each destination each month. The objective is to minimize the total shipping cost. Answer the following questions:
(a) Formulate this transportation problem as an LP. Clearly explain your variables and constraints.
(b) Use the Northwest corner method to ﬁnd an initial BFS.
(c) Starting from the initial BFS in part (b), apply the transportation algorithm to solve this problem.

Expert Solution

Colby Messinger answered 6 months ago

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