**BUS-660 ****Topic 8 Simulation Homework**

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**BUS-660 ****Topic 8 Simulation – Homework**

**Problem 16-07 (Algorithmic)**

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 are playing the Minnesota Twins 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, the probabilities of Atlanta winning each game are as follows:

Game |
1 | 2 | 3 | 4 | 5 | 6 | 7 |

Probability of Win |
0.7 | 0.45 | 0.49 | 0.55 | 0.47 | 0.45 | 0.6 |

- Set up a spreadsheet simulation model in whether Atlanta wins each game is a random variable. What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.
- What is the average number of games played regardless of winner? If required, round your answer to one decimal place.

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**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.

- 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)?
- 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))?

Average profit is _____________ the profit corresponding to average demand.

- 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.

50,000-unit production quantity: $____________

70,000-unit production quantity: $____________

- 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.

50,000 units: ____________

60,000 units: ____________

70,000 units: ____________

What is your recommendation?

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

**Problem 16-09**

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.

Player |
Iowa Energy |
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] |

- 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.

Average = ____________

Standard Deviation = ____________

What is the shape of the distribution of points scored by the Iowa Energy? ____________

- 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? ____________

- 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?

____________

- 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.

__________

- 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 1’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?

Average = ____________

Standard Deviation = ____________

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

**Problem 16-13 (Algorithmic)**

The wedding date for a couple is quickly approaching, and the wedding planner must provide the caterer an estimate of how many people will attend the reception so that the appropriate quantity of food is prepared for the buffet. The following table contains information on the number of RSVP guests for the 145 invitations. Unfortunately, the number of guests does not always correspond to the number of RSVPed guests.

Based on her experience, the wedding planner knows it is extremely rare for guests to attend a wedding if they notified that they will not be attending. Therefore, the wedding planner will assume that no one from these 50 invitations will attend. The wedding planner estimates that the each of the 25 guests planning to come solo has a 75% chance of attending alone, a 20% chance of not attending, and a 5% chance of bringing a companion. For each of the 60 RSVPs who plan to bring a companion, there is a 90% chance that she or he will attend with a companion, a 5% chance of attending solo, and a 5% chance of not attending at all. For the 10 people who have not responded, the wedding planner assumes that there is an 80% chance that each will not attend, a 15% chance each will attend alone, and a 5% chance each will attend with a companion.

RSVped Guests |
Number of invitations |

0 | 50 |

1 | 25 |

2 | 60 |

No response | 10 |

- Assist the wedding planner by constructing a spreadsheet simulation model to determine the expected number of guests who will attend the reception. Round your answer to 2 decimal places.
- To be accommodating hosts, the couple has instructed the wedding planner to use the Monte Carlo simulation model to determine
*X*, the minimum number of guests for which the caterer should prepare the meal, so that there is at least a 90% chance that the actual attendance is less than or equal to*X*. What is the best estimate for the value of X? Round your answer to the neares whole number.

**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 $1 per 100 miles short of 30,000.

- For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.

- What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.

- 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 16-05**

To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3400, and the average first-year commission for each new account opened is $6000. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.

- Determine the equation for computing Gustin’s profit per seminar, given values of the relevant parameters. Round your answers to the nearest dollar.
- What type of random variable is the number of new accounts opened? (
*Hint*: Review Appendix 16.1 for descriptions of various types of probability distributions.)

- Assume that the number of new accouts you get randomly is:

Simulation Trial |
New Accounts |

1 | 0 |

2 | 2 |

3 | 1 |

4 | 0 |

5 | 0 |

6 | 0 |

7 | 2 |

8 | 0 |

9 | 1 |

10 | 0 |

11 | 1 |

12 | 1 |

13 | 0 |

14 | 0 |

15 | 0 |

16 | 1 |

17 | 0 |

18 | 0 |

19 | 1 |

20 | 0 |

21 | 0 |

22 | 0 |

23 | 0 |

24 | 1 |

25 | 0 |

Construct a spreadsheet simulation model to analyze the profitability of Gustin’s seminars. Round the answer for the expected profit to the nearest dollar. Round the answer for the probability of a loss to 2 decimal places.

- How large of an audience does Gustin need before a seminar’s expected profit is greater than zero? Use Trial-and-error method to answer the question. Round your answer to the nearest whole number.

**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:

ProcurementCost ($) |
Probability |
Labor Cost ($) |
Probability |
TransportationCost ($) |
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 |

- Compute profit per unit for the base-case, worst-case, and best-case.

Profit per unit for the base-case: $

Profit per unit for the worst-case: $

Profit per unit for the best-case: $

- Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.

Mean profit per unit = $

- Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?

- Management believes the project may not be sustainable if the profit per unit is less than $5. Use simulation to estimate the probability the profit per unit will be less than $5. If required, round your answer to two decimal places.

**Problem 16-15 (Algorithmic)**

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $160,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $150,000.

- Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $130,000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $130,000? Round your answer to 1 decimal place. Enter your answer as a percent.
- How much does Strassel need to bid to be assured of obtaining the property?

What is the profit associated with this bid?

- Use the simulation model to compute the profit for each trial of the simulation run. With maximization of profit as Strassel’s objective, use simulation to evaluate Strassel’s bid alternatives of $130,000, $140,000, or $150,000. What is the recommended bid, and what is the expected profit?

A bid of ______________- results in the largest mean profit of $ ___________.

**Course**: BUS-660 Quantitative Methods

**School**: Grand Canyon University

- 17/04/2023
- 200