General Ford has two plants, two warehouses, and three customers. The locations
ID: 3183608 • Letter: G
Question
General Ford has two plants, two warehouses, and three customers. The locations of these are as follows:
Plants: Detroit and Atlanta
Warehouses: Denver and New York
Customers: Los Angeles, Chicago, and Philadelphia
Cars are produced at plants, then shipped to warehouses, and finally shipped to customers. Detroit can produce 150 cars per week, and Atlanta can produce 100 cars per week. Los Angeles requires 80 cars per week; Chicago, 70; and Philadelphia, 60. It costs $10,000 to produce a car at each plant, and the cost of shipping a car between two cities is given in Table 62. Determine how to meet General Ford’s weekly demands at minimum cost.
Table 62
To ($)
From
Denver
New York
Detroit
1253
637
Atlanta
1398
841
To ($)
From
Los Angeles
Chicago
Philadelphia
Denver
1059
996
1691
New York
2786
802
100
To ($)
From
Denver
New York
Detroit
1253
637
Atlanta
1398
841
Explanation / Answer
Its linear programming problem.
Production cost = 150 *10000 +100*10000 = 1500000 + 1000000 = $2500000
Shipping cost = 150*1253 +150*150*637 + 100*1398 +100*841 +250*1059 +250* 2786 + 250*996 + 250 * 802 + 250*1691 + 250 * 100
1059x +2786y where x+y = 80
996x+802y where x+y = 70
1691x+100y where x+y = 60
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