An electronics firm has production plants in Oregon and Tennessee. It ships its products overseas from three ports: Los Angeles, New Orleans, and New York. Transportation costs between plants and seaports are shown in the table.
|
Oregon
|
Los Angeles
$14
|
New Orleans
$26
|
New York
$30
|
|
Tennessee
|
24
|
10
|
12
|
The maximum capacity of the Oregon plant is 9,000 tons; the capacity of the Tennessee plant is 10,000 tons. The minimum daily quantities shipped overseas from Los Angeles, New Orleans, and New York are 5,000, 7,000, and 6,000 tons, respectively.
a. The company's objective is to minimize the cost of transporting its product from plants to ports while fulfilling its daily overseas shipping requirements. Formulate the appropriate LP problem.
b. Attempt to solve the LP problem by inspection. Find the company's minimum-cost transport plan using a standard LP computer program.
c. Find and interpret the shadow price associated with the 6,000 minimum daily shipment to New York.