3. Then read the following scenario and answer the questions that follow it: SCENERIO The Forest Stewardship Council {FSC} was form ed 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 talten from was managed according to its guidelines.3oon thereafter, several builders in California began to specialize in the construction of r'Illreen'II buildings that only used FEE-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 large inventories. 0n the other hand. builders who only used 'traditional'II wood which was not FSCcertified could order on ajust-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 40,000 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 hoardfoot. Atthe end ofa 3-month period the wood will dry and may warp, reducing its value. Dfany 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 4% 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 $3.35 per board foot. In addition, the green builder assigns a shortage cost of $100 per board foot for the loss of good will and damage to his reputation. How many board feet ofFSC certified lumber should the builder purchase? 2. 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 hoard foot for FEEcertified wood and sellit to the builder for $4.20 per board foot. Ifdemand exceeds the inventory, the green builder will buy traditional wood from a different lumber yard to meet the demand at price of$3.20 per boardfoot.In addition to the lost sale, Nice assigns a cost of $2.00 per board foot of sh ortage of F30 lumber. Ifthe inventory of FSC-certified lumber exceeds demand. Nice will immediately substitute the excess FSC certified lumber to m eet demand from other customers and reduce its purchases of traditional lumber accordingly. Nice pays $3.20 per board foot for traditional lumber. How many board feetof FSC certified lumber should Nice Lumber purchase