1. Virtual Reality Goggle Inventory. Galaxy Co. sells virtual reality (VR)
goggles, particularly targeting customers who like to play video
games. Galaxy procures each pair of goggles for $150 from its
supplier and sells each pair of goggles for $300. Monthly demand for
the VR goggles is a normal random variable with a mean of 160 units
and a standard deviation of 40 units. At the beginning of each month,
Galaxy orders enough goggles from its supplier to bring the inventory
level up to 140 goggles. If the monthly demand is less than 140, Galaxy
pays $20 per pair of goggles that remains in inventory at the end of
the month. If the monthly demand exceeds 140, Galaxy sells only the
140 pairs of goggles in stock. Galaxy assigns a shortage cost of $40 for
each unit of demand that is unsatisfied to represent a loss-of-goodwill
among its customers. Management would like to use a simulation
model to analyze this situation.
a. What is the average monthly profit resulting from its policy of
stocking 140 pairs of goggles at the beginning of each month?
b. What is the proportion of months in which demand is
completely satisfied?
c. Use the simulation model to compare the profitability of
monthly replenishment levels of 140 and 160 pairs of goggles.
Use a 95% confidence interval on the difference between the
average profit that each replenishment level generates to make
your comparison.
2. Dice Rolls. Construct a spreadsheet simulation model to simulate
1,000 rolls of a die with the six sides numbered 1, 2, 3, 4, 5, and 6.
a. Construct a histogram of the 1,000 observed dice rolls.
SHOW ANSWER
b. For each roll of two dice, record the sum of the dice. Construct a
histogram of the 1,000 observations of the sum of two dice.
SHOW ANSWER
c. For each roll of three dice, record the sum of the dice. Construct
a histogram of the 1,000 observations of the sum of three dice.
SHOW ANSWER
d. For each roll of four dice, record the sum of the dice. Construct a
histogram of the 1,000 observations of the sum of four dice.
SHOW ANSWER
e. Compare the histograms in parts (a), (b), (c), and (d). What
statistical phenomenon does this sequence of charts illustrate?
SHOW ANSWER
3.
Wearable Electronic Product Launch. The management of Madeira
Computing is considering the introduction of a wearable electronic
device with the functionality of a laptop computer and phone. The
fixed cost to launch this new product is $300,000. The variable cost
for the product is expected to be between $160 and $240, with a most
https://college.cengage.com/nextbook/business/camm_180959/student/data_files/chapter_11/madeira.xlsx
https://college.cengage.com/nextbook/business/camm_180959/student/data_files/chapter_11/madeira.xlsx
likely value of $200 per unit. The product will sell for $300 per unit.
Demand for the product is expected to range from 0 to approximately
20,000 units, with 4,000 units the most likely.
a. Develop a what-if spreadsheet model computing profit for this
product in the base-case, worst-case, and best-case scenarios.
b. Model the variable cost as a uniform random variable with a
minimum of $160 and a maximum of $240. Model the product
demand as 1,000 times the value of a gamma random variable
with an alpha parameter of 3 and a beta parameter of 2.
Construct a simulation model to estimate the average profit and
the probability that the project will result in a loss.
c. What is your recommendation regarding whether to launch the
product?
4.
Profitability of New Product. The management of Brinkley
Corporation is interested in using simulation to estimate the profit
per unit for a new product. The selling price for the product will be
$45 per unit. Probability distributions for the purchase cost, the labor
cost, and the transportation cost are estimated as follows:
https://college.cengage.com/nextbook/business/camm_180959/student/data_files/chapter_11/brinkley.xlsx
https://college.cengage.com/nextbook/business/camm_180959/student/data_files/chapter_11/brinkley.xlsx
a. Construct a simulation model to estimate the average profit per
unit. What is a 95% confidence interval around this average?
b. Management believes that the project may not be sustainable if
the profit per unit is less than $5. Use simulation to estimate the
probability that the profit per unit will be less than $5. What is a
95% confidence interval around this proportion?
5.
Estimating Auto Accident Costs. Statewide Auto Insurance believes
that for every trip longer than 10 minutes that a teenager drives,
there is a 1 in 1,000 chance that the drive will result in an auto
accident. Assume that the cost of an accident can be modeled with a
beta distribution with an alpha parameter of 1.5, a beta parameter of
3, a minimum value of $500, and a maximum value of $20,000.
Procurement
Cost ($)
Probability Labor
Cost
($)
Probability Tran
C
10 0.25 20 0.10
11 0.45 22 0.25
12 0.30 24 0.35
25 0.30
https://college.cengage.com/nextbook/business/camm_180959/student/data_files/chapter_11/statewide.xlsx
https://college.cengage.com/nextbook/business/camm_180959/student/data_files/chapter_11/statewide.xlsx
Construct a simulation model to answer the following questions.
(Hint: Review Appendix 11.1 for descriptions of various types of
probability distributions to identify the appropriate way to model the
number of accidents in 500 trips.)
a. If a teenager drives 500 trips longer than 10 minutes, what is the
average cost resulting from accidents? Provide a 95% confidence
interval on this mean.
b. If a teenager drives 500 trips longer than 10 minutes, what is the
probability that the total cost from accidents will exceed $8,000?
Provide a 95% confidence interval on this proportion.
6. Automobile Collision Claims. State Farm Insurance has developed
the following table to describe the distribution of automobile collision
claims paid during the past year.
a. Set up a table of intervals of random numbers that can be used
with the Excel VLOOKUP function to generate values for
automobile collision claim payments.
b. Construct a simulation model to estimate the average claim
payment amount and the standard deviation in the claim
payment amounts.
c. Chapter 4 describes the analytical calculation of the mean and
standard deviation of a random variable.
Let X be the discrete random variable representing the dollar
value of an automobile collision claim payment. Let,
represent possible values of X. Then, the mean
and standard deviation of X can be computed as
, and
x1, x2, … , xn (μ)
(σ)
μ = x1 × P(X = x1) + ⋯ + xn × P(X = xn)
.
Compare the values of sample mean and sample standard
deviation in part (b) to the analytical calculation of the mean
and standard deviation. How can we improve the accuracy of
the sample estimates from the simulation?
7.
Playoff Series in National Basketball Association. The Dallas
Mavericks and the Golden State Warriors are two teams in the
σ = √(x1 − μ)2 × P(X = x1) + ⋯ + (xn − μ)2 × P(X = xn)
Payment($) Probability
0 0.83
500 0.06
1,000 0.05
2,000 0.02
5,000 0.02
8,000 0.01
10,000 0.01
