(ANSWER) BUS 660 Topic 8 Simulation – Homework

BUS 660 Topic 8 Simulation – Homework

Problem 16-03: Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer Si per 100 miles short of 30,000.

1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.
2. What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.
3. What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00? If required, round your answer to the hundreds place.

Problem 16-09: The Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the National Basketball Association Developmental League (NBA-DL). Because a player in the NBA-DL is still developing their skills, the number of points he scores in a game can vary. Assume that each player’s point production can be represented as an integer uniform variable with the ranges provided in the table below.

1. Develop a spreadsheet model that simulates the points scored by each team. Use at least 1,000 trials. What is the average and standard deviation of points scored by the Iowa Energy? If required, round your answer to one decimal place. What is the shape of the distribution of points scored by the Iowa Energy?
2. b. What is the average and standard deviation of points scored by the Maine Red Claws? If required, round your answer to one decimal place. Average = Standard Deviation = What is the shape of the distribution of points scored by the Maine Red Claws,
3. Let Point Differential = Iowa Energy points – Maine Red Claw points. What is the average point differential between the Iowa Energy and Maine Red Claws? If required, round your answer to one decimal place. What is the standard deviation in the point differential? What is the shape of the point differential distribution?
4. What is the probability of that the Iowa Energy scores more points than the Maine Red Claws? If required, round your answer to three decimal places.
5. The coach of the Iowa Energy feels that they are the underdog and is considering a “riskier” game strategy. The effect of the riskier game strategy is that the range of each Energy player’s point production increases symmetrically so that the new range is [0, original upper bound + original lower bound]. For example, Energy player l’s range with the risky strategy is [0, 25]. How does the new strategy affect the average and standard deviation of the Energy point total? How is the probability of the Iowa Energy scoring more points that the Maine Red Claws affected? If required, round your answer to three decimal places.

Problem 16-11 (Algorithmic): 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 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.

1. Create a what-if spreadsheet model using a formula that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand (60,000 units)?
2. 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 associated with the production quantity of 60,000 dolls? Round your answer to the nearest dollar. How does this compare to the profit corresponding to the average demand (as computed in part (a))?
3. 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. What is the mean profit associated with each? Round your answers to the nearest dollar.
4. In addition to mean profit, what other factors should FTC consider in determining a production quantity? The input in the box below will not be graded, but may be reviewed and considered by your instructor. Compare the three production quantities (50,000, 60,000, and 70,000) using all these factors. What trade-offs occur? Round your answers to 3 decimal places. What is your recommendation? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Problem 16-01: 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:

1. Compute profit per