1 The S&P Stock 500 Exchange index had the following values in January 2012. A. Is there statistical evidence of a trend over this time period? Date S&P 500 index 04-jan-12 1,277.30 05 1,281.06 06 1,277.81 09 1,280.70 10 1,292.08 11 1,292.48 12 1,295.50 13 1,289.09 17 1,293.67 18 1,308.04 19 1,314.50 20 1,315.38 23 1,316.00 24 1,314.65 25 1,326.06 26 1,318.43 B. What would be the predicted value for the index for the next business day after January 26? C. What is the 95% prediction interval for the next business day? Problem 2 Perishable Product Pricing We have 3,000 units of product to sell over a five day period. From historical sales data, we have estimated the following demand curves: P=price/unit in $, Q=number of units sold. Day 1: P=10-0.01Q Valid for prices between $3 and $8. Day 2: same as Day 1. Day 3: P=15-0.01Q Valid for prices between $6 and $10 Day 4: P=20-0.01Q Valid for prices between $6 and $12 Day 5: same as Day 1. A. Formulate as a Solver problem in Excel. What are the revenue maximizing prices for days 1-5? What is the maximum possible revenue? B. If the price must be the same on each day, what is the revenue maximizing price? What is the revenue? What is the revenue penalty for operating a fixed price policy? C. Suppose that on Day 1, we post the optimal price(from A above) but sales are 10% above estimate demand. Re-solve the problem computing new optimal prices for Days 2-5 assuming demand is 10% above expected each day except the last day. What is the revenue? D. Repeat Q3 with an assumption of a fixed single price for the five days. What is the revenue? Again. Compute the revenue penalty for operating a fixed price policy. E. Is 3,000 the optimal number of units to order? Would you order more or fewer? F. Repeat question 3 and 4 under an assumption that demand is 10% below expected each day except the last. Assume inventory-clearing prices on the last day. What is the revenue penalty from fixed pricing