3. Then read the following scenario and answer the questions that follow it: SCENARIO 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 . Consider the following 3 scenarios and related questions 1 . 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 15,000 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. 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. How many board feet of FSC certified lumber should the builder purchase ? Board Feet = Mean + Z*StdDev Cu = 4 - 3.40 + 2 = 2.6 Co = 4 - 2 + .04*4 = 2.16 SL = 2.6/(2.6+2.16) = 0.5462 Z = normsinv(.5462) = .116 Board Feet = 35000 + .116*15000 = 36,740