(a) Sunco Oil produces oil at two wells. Well 1 can produce as many as 150,000 barrels per day, and Well 2 can produce as many as 200,000 barrels per day. It is possible to ship oil directly the wells to Sunco's customers in Los Angeles and New York. Alternatively, Sunco could transport oil to the ports of Mobile and Galveston and then ship it by tank to New York or Los Angeles. Los Angeles requires 160,000 barrels per day, and New York requires 140,000 barrels per day. The cost of shipping 1,000 barrels between two points are shown in the table below. Formulate a transshipment model to minimize the transport costs in meeting the oil demands of Los Angeles and New York.
|
From
|
To ($)
|
|
Well 1
|
Well 2
|
Mobile
|
Galveston
|
N.Y.
|
L.A.
|
|
Well 1
|
0
|
---
|
10
|
13
|
25
|
28
|
|
Well 2
|
---
|
0
|
15
|
12
|
26
|
25
|
|
Mobile
|
---
|
---
|
0
|
6
|
16
|
17
|
|
Galveston
|
---
|
---
|
6
|
0
|
14
|
16
|
|
N.Y.
|
---
|
---
|
---
|
---
|
0
|
15
|
|
L.A.
|
---
|
---
|
---
|
---
|
15
|
0
|
(b) In (a), assume that before being shipped to Los Angeles or New York, all oil produced at the wells must be refined at either Galveston or Mobile. To refine 1,000 barrels of oil costs $12 at Mobile and $10 at Galveston. Assuming that both Mobile and Galveston have infinite capacity, reformulate the problem to minimize the daily cost of transporting and refining the oil requirements of Los Angeles and New York.