Operations management simulation 3 questions only answers needed

see attached file

Major League Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, suppose the probabilities of Atlanta winning each game are as follows.

Game1234567Probability of Win0.590.540.470.460.470.540.51

Construct a simulation model in which whether Atlanta wins or loses each game is a random variable. Use the model to answer the following questions. (Use at least 1,000 trials.)

(a)
What is the average number of games played regardless of winner? (Round your answer to one decimal place.)
games

(b)
What is the probability that the Atlanta Braves win the World Series? (Round your answer to three decimal places.)

The Iowa Wolves are 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. Develop a spreadsheet model that simulates the points scored by each team. Assume that each player's point production can be represented as an integer uniform variable with the ranges provided in the following table. (Use at least 1,000 trials.)

PlayerIowa WolvesMaine Red Claws1[5, 20][6, 12]2[7, 20][15, 20]3[5, 10][10, 20]4[10, 40][15, 30]5[7, 20][6, 10]6[2, 10][1, 20]7[2, 5][1, 4]8[2, 4][2, 4]

(a)
Consider the points scored by the Iowa Wolves team. (Round your answers to two decimal places.)
What is the average of points scored?

What is the standard deviation?

What is the shape of the distribution?
uniformbell-shaped skewed leftskewed right

(b)
Consider the points scored by the Maine Red Claws. (Round your answers to two decimal places.)
What is the average of points scored?

What is the standard deviation?

What is the shape of the distribution?
uniformbell-shaped skewed leftskewed right

(c)
Let Point Differential = Iowa Wolves points − Maine Red Claw points. (Round your answers to two decimal places.)
What is the average point differential between the Iowa Wolves and Maine Red Claws?

What is the standard deviation in the point differential?

What is the shape of the point differential distribution?
uniformbell-shaped skewed leftskewed right

(d)
What is the probability that the Iowa Wolves scores more points than the Maine Red Claws? (Round your answer to three decimal places.)

(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? (Round your answers to two decimal places.)
average pointsstandard deviation points
What is the new probability of the Iowa Wolves scoring more points than the Maine Red Claws? (Round your answer to three decimal places.)

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 $33 per doll. During the holiday selling season, FTC will sell the dolls for $41 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 extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution 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.

(a)
Determine the equation for computing FTC's profit for given values of the relevant parameters (e.g., demand, production quantity, etc.).
Using this equation, compute FTC's profit (in dollars) when realized demand is equal to 60,000 (the average demand).
$  

(b)
Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, simulate the sales of the Dougie doll using a production quantity of 60,000 units.
What is the estimate of the average profit (in dollars) associated with the production quantity of 60,000 dolls? (Use at least 1,000 trials. Round your answer to the nearest integer.)
$  

(c)
Compare the average profit estimated by simulation in part (b) to the profit calculation in part (a).
The average profit from the simulation is greater than the profit computed in part (a)The average profit from the simulation is less than the profit computed in part (a).
Explain why they differ.
Since the demand is being modeled as a normal random variable, the sample mean profit will always tend to be higher than the true mean profit.Since the demand is being modeled as a normal random variable, the sample mean profit will always tend to be lower than the true mean profit. Profit is limited by the production quantity, so higher than average demand does not correspond to higher profits, but lower demand will lead to lower profits.Profit is limited by the production quantity, so lower than average demand does not correspond to lower profits, but higher demand will lead to higher profits.

(d)
Before making a final decision on the production quantity, management wants an analysis of a more aggressive 70,000-unit production quantity and a more conservative 50,000-unit production quantity. Run your simulation with these two production quantities. (Use at least 1,000 trials. Round your answers to the nearest integer.)
What is the mean profit (in dollars) associated with 50,000 units?
$  
What is the mean profit (in dollars) associated with 70,000 units?
$  

(e)
In addition to mean profit, what other factors should FTC consider in determining a production quantity? (Select all that apply.)
probability of a lossgut feelingprobability of a shortagestock marketprofit standard deviation