and
The Big Bang Theory
Assume the hours needed to cook a meal or done a basket of laundry
are different, and they are described in the table.
1. Suppose each person has 12 hours for the two tasks in a week, and suppose both Sheldon and
Leonard each spend 6 hours on cooking and 6 hours on laundry. Consider an offer from Leonard to
Sheldon: do 3 baskets of laundry for me each week, and I'll cook you 2 meals. Can you find a production
plan such that the offer benefits both Leonard and Sheldon? Hint: For a production plan, you need to
specify how each person divides his 12 hours between the two tasks. The offer benefits Sheldon (or
Leonard) when it results in no fewer meals and no fewer baskets for him.
2. Consider the same setup in question 1. Consider another offer from Leonard to Sheldon: do 1 basket of
laundry for me each week, and I'll cook you 3 meals. Can you find a production plan such that the offer
benefits both Leonard and Sheldon? Explain.
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