A young couple, Eve and Steven, want to divide their four main household chores so that each is responsible for two of them but the total time spent on housework is kept to a minimum. The table below shows how many hours each partner requires for each task.
|
|
Hours Required for each Task
|
|
Partner
|
Marketing
|
Cooking
|
Cleaning
|
Laundering
|
|
Eve
|
3.2
|
7.4
|
4.1
|
2.5
|
|
Steven
|
4.0
|
6.8
|
4.5
|
2.7
|
i) formulate and solve an integer program to determine who does what.
ii) modify the formulation by adding a constraint that whoever does the cleaning should not also do the marketing. Re-solve the modified formulation.