General Ford has two plants, two warehouses, and three customers. The locations
ID: 3121755 • 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
Understanding the Decision variables first :
Let DD represent cars shipped from Detroit to Denver.
Let DN represent cars shipped from Detroit to NY.
Let AD represent cars shipped from Atlanta to Denver.
Let AN represent cars shipped from Atlanta to NY.
Similarly we have DL,DC,DP and NL,NC,NP to represent shipping from warehouses to the customer.
We have the Objective function :Minimize Cost Z =
1253*DD+637*DN+1398*AD+841*AN+1059*DL+996*DC+1691*DP+2786*NL+802*NC+100*NP +10000*(DD+DN+AD+AN).
This contains both Shipping and Production costs !
Subject to the constraints that determine plant capacity.
DD+DN<=150 : Detroit Plant Capacity
AD+AN<=100 : Atlanta Plant Capacity
Requirement Constraints from LA,Chicago and Philly:
LA:80 ; DL+NL = 80
Chicago:70 ; DC+NC=70
Philly:60 ; DP+NP = 60
So we have the Objective function to be minimized and subject to 5 contraints in total along with non negativity constraints on the variables.We can use Excel Solver or LiPS easily to get the solution.
The Question only asks us to set-up the problem and not actually solve it.So I will stop with the formulation.
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