Problem 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?
