Scenario 2A: Builder's Order (FSC) A green builder must decide how much FSC lumber to purchase to meet demand for the next 3 months. Demand is normally distributed with a mean of 35,000 board-feet and a standard deviation of 17,000 board feet. (A board-foot is a standard unit for lumber.) The purchase price for the builder is $4.00 per board-foot. At the end of a 3-month period the wood will dry and may warp, reducing its value. Of any lumber remaining in the builder's lumber yard at the end of the 3-month period, approximately half will be worthless. The builder will use any wood that is not warped in the next period. However, buying the wood now, rather than in the next period incurs a holding cost of 3% of the purchase cost. (Only apply this to the wood that is held over for the following period, and not to the wood that is thrown away.) If the builder has too little FSC certified wood to meet demand, he will be forced to substitute traditional lumber, which he can buy for $3.40 per board foot. In addition, the green builder assigns a shortage cost of $2.00 per board foot for the loss of good will and damage to his reputation.

A. How many board feet of FSC certified lumber should the builder purchase?

Scenario 2B: Middle-man's Order (1 customer) Suppose a lumber-yard (Nice Lumber) agrees to serve as a distributor for a builder. This means Nice Lumber will stock the FSC-certified lumber for one green builder. Nice Lumber will pay $4.00 per board foot for FSC-certified wood and sell it to the builder for $4.25 per board foot. If demand exceeds the inventory, the green builder will buy traditional wood from a different lumber yard to meet the demand at a price of $3.40 per board-foot. In addition to the lost sale, Nice assigns a cost of $2.00 per board foot of shortage of FSC lumber. If the inventory of FSC-certified lumber exceeds demand, Nice will immediately substitute the excess FSC certified lumber to meet demand from other customers and reduce its purchases of traditional lumber accordingly. Nice pays $3.40 per board foot for traditional lumber.

B. How many board-feet of FSC certified lumber should Nice Lumber purchase?