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McTavish Cleaning Inc. provides a basic house-cleaning service to stressed-out trainee executives. This basic house-cleaning service includes four components, namely, vacuuming, kitchen-cleaning, bathroom-cleaning, and general straightening-up. McTavish employs a total of five maid-persons and wants to allocate four of them to its basic house-cleaning service with the objective of minimizing the total time it takes to provide the service. The time (measured in hours) it takes each maid-person to provide each component is listed in the following table:
Vacuum Kitchen Bathroom Straighten-Up
Harold 6 5 2 1
Betsy 9 8 7 3
Mildred 8 5 9 4
Jennifer 7 7 8 3
George 5 5 6 4
i) Use the Hungarian Method to determine how McTavish should allocate their staff in order to minimize the total time that it takes to provide the basic house-cleaning service.
ii) What is the minimum total time that it takes to provide the basic house-cleaning service?
iii) Would your answers to parts i) and ii) change if George were to refuse to do any more vacuuming? If so, how?
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