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.
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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.
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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.
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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.
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e. Compare the histograms in parts (a), (b), (c), and (d). What
statistical phenomenon does this sequence of charts illustrate?
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