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What is the maximum number of selling transactions

Baseline information:
The local real estate agent in your community estimates that it takes 120 days on average to sell a house; whereas this number changes some with the economy and season, it has been fairly stable over the past decade. You observe from monitoring the classified ads that over the past year the number of houses for sale has ranged from 20 to 55 at any point in time, with an average of 40.
Q1:
Without reducing the average selling completion time, what is the maximum number of selling transactions per year achieving a desired lower average of 30 active transactions at any point in time?
Q2
Without reducing the total number of transactions per year, what is the maximum average transaction completion time achieving a desired lower average of 30 active transactions at any point in

Solution:

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