Reference no: EM1318005
Define Transportation problem.
The Greenberg public hearing meeting turned stormy. Citizens from four suburbs were gathered at city hall to try to get the city's federal funds for their own suburbs. The government recently awarded $750,000 to the city for road improvements. The city requested bids and five contractors submitted bids for work in the four suburbs. The bids are listed in Table (in thousands of dollars).
Table Bids $000s
|
Contractor
|
Suburb
|
|
|
1
|
2
|
3
|
4
|
|
A
|
210
|
242
|
202
|
243
|
|
B
|
222
|
232
|
205
|
250
|
|
C
|
205
|
225
|
244
|
210
|
|
D
|
265
|
206
|
200
|
270
|
|
E
|
215
|
211
|
253
|
212
|
Because under the terms of the federal grant, the work must be completed fairly soon, none of the contractors are large enough to perform more than one job. That is, it will be necessary to use a different contractor for each suburb's job. From the bids, it was clear to Greenberg's city council that the federal funds would not cover road improvements in all four suburbs. As they began to analyze the situation, they realized they needed some hard facts. Therefore, they called the operations director of Greenberg and requested the following information.
a. What is the minimum amount of money that the city must add to the government grant such that work may be done in all four suburbs?
b. What is the best contractor-to-suburb match?
c. Which of the contractors should not receive a job contract?
d. If the city cannot come up with any supplementary funds, only three suburbs will be repaired. Based on dollars and cents, which three suburbs should be selected such that the surplus from the government grant is maximized?
To provide the above information, prepare an LP formulation for this assignment problem and solve. Then, discuss the answers to the above questions.