Problem
The Forest Stewardship Council (FSC) was formed in 1993 to promote sustainable management of the world's forests. The FSC quickly began to certify lumber based on whether the forest that it was taken from was managed according to its guidelines. Soon thereafter, several builders in California began to specialize in the construction of "Green" buildings that only used FSC certified lumber. This was seen as a viable business because some customers were willing to pay a premium to have their projects completed with FSC lumber. These builders have an opportunity to order this lumber once every 3 months because the forests involved must be harvested in accordance with certain restrictions. Consequently, builders who focused on this market were forced to hold larger inventories. On the other hand, builders who only used "traditional" wood which was not FSC-certified could order on a just-in-time basis, meaning they did not have to hold any lumber in their own lumberyards.
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.
• How many board-feet of FSC certified lumber should Nice Lumber purchase?
Suppose Nice Lumber will stock the FSC certified lumber for 12 green builders. For each of these builders, demand is normally distributed with a mean of 35,000 board feet and a standard deviation of 17,000 board feet, and each builder's demand is independent of other builders' demand.
• How many board-feet of FSC certified lumber should Nice Lumber purchase per builder?