2. A carpet company sells and installs floor covering for commercial buildings.
ID: 3122172 • Letter: 2
Question
2. A carpet company sells and installs floor covering for commercial buildings. The company was awarded a contract for four jobs. The company needs to assign an installation crew to each of the four jobs. Currently, four installation crews are available for assignment. Each crew is identified by a color code. The following table shows the time required (in hours) for each crew to complete each of the four jobs:
Time Required in Hours
Job 1 Job 2 Job 3 Job 4
_____________________________________________
Red 32 36 27 35
White 40 28 36 42
Crew Blue 30 38 28 38
Green 30 32 36 42
The company wants to assign either Blue Crew or White Crew to Job 2 because of customer preference. It does not want to assign Green Crew to Job 4 because of quality considerations.
The objective is to minimize the total cost of all assignments.
(c) Determine all the constraints. Briefly describe what each constraint represents.
Explanation / Answer
Assume that,
Hourly rate for each crew is 1 $/hour
Job 1 Job 2 Job 3 Job 4
_____________________________________________
Red 32 36 27 35
White 40 28 36 42
Crew Blue 30 38 28 38
Green 30 32 36 42
To mininmize the cost of assignment minimum hours should be required, based on given table minimum hours of each crew are:
Red-27
White-28
Blue-28
Green-30
Total hour are 113 hours, so minimum cost of assignment can be 113 $ but because of given considtions:
Condition 1: Either White or Blue crew should be assigned to JOB-2
Constraint 1: White crew is assigned JOB-2 as out of both White crew was taking less number of hours to complete JOB-2 which is 28Hours
Considtion 2: Green should not be assigned JOB-4
Constraint 2: Green crew is assigned JOB-1 as out of alll the crews Green takes less time to complete which is 30 Hour
Constraint 3: Blue is assigned JOB-3 as bluw is taking minimum hours in completing JOB-3 which is 28Hours due to which Red crew is assigned JOB-4 where red crew is taking 35 Hours hence the total hours to complete the assignement are:
RED: 35
WHITE: 28
BLUE: 28
GREEN: 30
Total is 121 Hours which is the minium with given conditions
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