Bars$-$on$-$Wheels, a bicycle maker makes a variety of good quality bikes. Its production facilities are exceptional, and it has about $30$ years$$ experience in making all kinds of non$-$motorized bikes. Wal$-$Mart buys nearly $90$ percent of its annual production of $50,000$ bikes. These are mostly basic, general$-$purpose bikes. The margin from sales to Wal$-$Mart is lower than the rest of the sales. In addition, Wal$-$Mart$$s business is not guaranteed$-$ Wal$-$Mart decides in January whether, and how many, bikes they will buy in the following year. This is one reason why the owners have not been able to decide whether to increase capacity to $100,000$ units.

Note: Please assume the role of consultant to Bars$-$on$-$Wheels. Ron, the owner of BOW, is an excellent negotiator of business deals. He does not like consultants much and has low tolerance for the obvious. The store manager of Wal$-$Mart, Catherine, is known to be a shrewd manager with plenty of acumen and understands her business very well and does not yield to $$smooth talking$.$