A service company provides lawn service, including mowing lawns and lawn care, landscaping, and lawn maintenance, to residential and commercial customers in the Draper town community. In the summer the company has three teams that it schedules daily for jobs. Team 1 has ve members, team 2 has four members, and team 3 has three members. On a normal summer day, the company will have approximately 14 jobs. Each team works 10 hours a day, but because of the heat plus work breaks, each team actually works only 45 minutes out of every hour. The following table shows the times (in minutes) and costs (in dollars) required for each team to complete the 14 jobs for a specie day.
Team 1 Team 2 Team 3
Job Time(min.) Cost($) Time(min.) Cost($) Time(min.) Cost($)
A 45 48 65 55 78 50
B 67 70 72 60 85 55
C 90 94 105 84 125 75
D 61 65 78 65 97 60
E 75 80 93 75 107 66
F 48 55 70 65 95 60
G 65 70 83 70 110 67
H 67 72 84 74 100 65
I 95 100 110 90 130 80
J 60 65 78 65 95 62
K 47 55 64 57 84 56
L 114 118 135 110 155 95
M 85 90 107 98 125 75
N 63 67 81 72 102 68
The company manager wants to develop a schedule of team assignments to the jobs for this day.
Formulate and solve a linear programming model to determine the assignments of 1
Teams to jobs that will minimize total job time for the day, given a daily budget of $ 1;
000.
Indicate how many minutes each crew will work during the day. Next, reformulate and solve this model if cost minimization is the objective. Of these two models, which one do you think the manger should select and why