(All answers were generated using 1,000 trials and native Excel functionality.)
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 $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:
Procurement
Cost ($)
Probability Labor
Cost ($)
Probability Transportation
Cost ($)
Probability
10 0.25 20 0.10 3 0.75
11 0.45 22 0.25 5 0.25
12 0.30 24 0.35
25 0.30
(a) Construct a simulation model to estimate the average profit per unit. What is a 95% confidence interval around this average?
Round your answers to two decimal places.
Lower Bound: $
Upper Bound: $
(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?
Round your answers to one decimal of a percentage.
Lower Bound: %
Upper Bound: %
2 0(All answers were generated using 1,000 trials and native Excel functionality.)
The Iowa Wolves is scheduled to play against the Maine Red Claws in an upcoming game in the National Basketball Association (NBA) G League. Because a player in the NBA G League is still developing his skills, the number of points he scores in a game can vary substantially. Assume that each player's point production can be represented as an integer uniform random variable with the ranges provided in the following table:
Player lowa Wolves Maine Red Claws
1 [5,20] [7,12]
2 [7,20] [15,20]
3 [5,10] [10,20]
4 [10,40] [15,30]
5 [6,20] [5,10]
6 [3,10] [1,20]
7 [2,5] [1,4]
8 [2,4] [2,4]
(a) Develop a spreadsheet model that simulates the points scored by each team and the difference in their point totals. What are the average and standard deviation of points scored by the Iowa Wolves?
Round your answers to one decimal place.
Average:
Standard Deviation:
What is the shape of the distribution of points scored by the Iowa Wolves?
(b) What are the average and standard deviation of points scored by the Maine Red Claws?
Round your answers to one decimal place.
Average:
Standard Deviation:
What is the shape of the distribution of points scored by the Maine Red Claws?
(c) Let Point Differential = Iowa Wolves points – Maine Red Claws points. What is the average Point Differential between the Iowa Wolves and Maine Red Claws? What is the standard deviation of the Point Differential? If your answer is negative, enter a minus sign in the input box.
Round your answers to one decimal place.
Average:
Standard Deviation:
What is the shape of the point differential distribution?
(d) What is the probability that the Iowa Wolves scores more points than the Maine Red Claws?
Round your answer to the nearest whole number.
%
(e) The coach of the Iowa Wolves feels that they are the underdog and is considering a riskier game strategy. The effect of this strategy is that the range of each Wolves player's point production increases symmetrically so that the new range is [0, original upper bound + original lower bound]. For example, Wolves player 1's range with the risky strategy is [0, 25]. How does the new strategy affect the average and standard deviation of the Wolves point total? How does that affect the probability of the Iowa Wolves scoring more points than the Maine Red Claws?
Round first two numerical answers to one decimal place and the last answer to a whole percentage.
The average Iowa Wolves point total will be points and the standard deviation of the Iowa Wolves point total will be points. The probability of the Iowa Wolves scoring more points than the Maine Red Claws will become %.
3 - (All answers were generated using 1,000 trials and native Excel functionality.)
In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is uncertain. The normal probability distribution with an average of 60,000 dolls and a standard deviation of 15,000 is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision.
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