Exam 14: Monte Carlo Simulation

According to the ___________, the sum of independent random variables can be approximated by a normal probability distribution.

The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as

Salemach Corporation is a start-up company that manufactures simple machines. It is interested in analyzing the profit from a new machine. It estimates that the selling price will be $150 per unit and the setup and advertising costs will total $250,000. The company estimates that the per unit raw material cost is uniformly distributed between $50 and $80 and are equally likely. The demand is normally distributed with a mean of 12,000 units and a standard deviation of 3000 units. The probability distribution for a range of labor cost per unit is given below. Labor Cost Probability \ 52 0.05 \ 53 0.25 \ 54 0.40 \ 55 0.25 \ 56 0.05 ​ a. Obtain estimates for the mean profit, maximum profit, minimum profit, and standard deviation of profit. b. What is your estimate of the probability of a loss?

All the values of computer-generated random numbers are

The quality of a device should be examined in the inspection department sequentially in three steps before it is sent to packaging department. The probability distributions for the time required to complete each of the activities are as follows: ​ Step Time (minutes) Probability 1 3 0.15 5 0.25 7 0.35 9 0.25 2 11 0.25 13 0.30 15 0.45 3 8 0.35 10 0.20 12 0.45 ​ a. Construct a spreadsheet simulation model to estimate the average time spent in inspection department and the standard deviation of the time spent in inspection department. b. What is the estimated probability that the inspection will be completed in 32 minutes or less?

The process of determining that a computer program implements a simulation model as it is intended is known as

The __________ function in Excel is used to compute the statistics required to create a histogram.

An entrepreneur who operates a cellular phone store orders inventory of cell phones based on four internal memory specifications - 8 GB, 16 GB, 32 GB, and 64 GB. She wants to evaluate her inventory ordering policy for the phones with four different amounts of internal memory. Any phone unsold at the end of a period is kept in inventory for the next sales period and incurs a holding cost expressed as 10% of the cost per unit per period. If demand during a period exceeds supply for a phone, then sale is lost. The data on the cost and selling prices of the cell phones categorized by these memory specifications are known, and representative data on the past sales are also available. $\begin{array} { | c | c | c | } \hline \text { Internal Memory } & \text { Cost (\$) } & \text { Selling Price (\$) } \\\hline \mathbf { 8 G B } & 420 & 430 \\\mathbf { 1 6 } \mathrm { GB } & 500 & 520 \\\mathbf { 3 2 } \mathrm { GB } & 590 & 620 \\\mathbf { 6 4 } \mathrm { GB } & 670 & 700 \\\hline\end{array}$ Past Sales: Period 1 276 274 327 332 2 302 211 264 329 3 299 276 306 239 4 261 258 232 277 5 260 244 278 220 6 306 252 262 252 7 227 213 290 253 8 228 217 308 250 9 205 215 246 277 10 236 237 272 284 11 279 251 301 282 12 303 271 271 282 13 266 252 276 317 14 263 306 285 310 15 210 250 328 253 16 247 230 317 340 17 314 285 289 332 18 283 304 312 256 19 283 245 294 272 20 252 237 262 323 a. Construct a spreadsheet simulation model to estimate the total profit the entrepreneur earns in a period when ordering 300 units of each cell phone. To model the respective cell phone demands, fit a realistic distribution to the sales data. What is the average total profit? What is the estimated likelihood that the entrepreneur makes less than $10,000 next period? b. Using Spearman rank correlation, compute the correlations between the demands for the cells phones based on the four memory specifications. Incorporate a correlation matrix to captures the interrelationships between the demands for each cell phone type. What is the average total profit? What is the estimated likelihood that the entrepreneur makes less than $10,000 next period? Comparing these answers to (a), conclude how the correlated demand affects the model's implications.

A set of values for the random variables is called a(n)

The type of distribution shown in the graph below is

An Investment firm offers free financial planning seminars at major hotels for groups of 30 individuals. Each seminar costs them $4,000 and the average first-year commission for each new enrollment is $6,000. The firm estimates that for each individual attending the seminar, there is a 0.05 probability that he/she will enroll. a. Determine the equation for computing the profit per seminar, given values of the relevant parameters. b. Construct a spreadsheet simulation model to analyze the profitability of the seminars. Would you recommend the investment firm to continue running the seminars?

The outcome of a simulation experiment is a(n)

The random variables corresponding to the interarrival times of customers and the service times of customers are commonly described by a(n) __________ distribution.

The manager of a company decides to arrange a party for being promoted and has invited 50 guests for dinner. The following table contains information on the number of RSVP'ed guests. He assumes that 12 people will not turn up. He also estimates that 13 guests planning to come solo has a 65 percent chance of attending alone, a 30 percent chance of not attending, and a 5 percent chance of bringing a companion. For each of the 20 guests who plan to bring a companion, there is a 75 percent chance that she or he will attend with a companion, a 10 percent chance of attending solo, and a 15 percent chance of not attending at all. For the 5 people who have not responded, the wedding planner assumes that there is an 85 percent chance that each will not attend, a 10 percent chance they will attend alone, and a 5 percent chance they will attend with a companion. ​ Guests Number of Invitations 0 12 1 13 2 20 No response 5 ​ a. Assist the manager by constructing a spreadsheet simulation model to determine the expected number of guests who will attend the party. b. Use the Monte Carlo simulation model to determine X, the minimum number of guests for whom the dinner needs to be ordered, so that there is at least a 95 percent chance that the actual attendance is less than or equal to X. What is the best estimate for the value of X?

A disadvantage of the simple what-if analyses is that

For a given mean and standard deviation, the ____________ function in Excel is used to generate a value for the random variable characterized by a normal distribution.

Which of the following parameters is required to convert a computer-generated random variable into a uniform random variable?

The stock price of Robin Tires, Inc., listed on the Stock Exchange is currently $20. The following probability distribution shows how the price per share is expected to change over a three-month period: ​ $\begin{array} { | c | c | } \hline \begin{array} { c } \text { Stock Profit } \\\text { Change (\$) }\end{array} & \text { Probability } \\\hline - 3 & 0.25 \\- 2 & 0.2 \\- 1 & 0.05 \\0 & 0.15 \\+ 1 & 0.1 \\+ 2 & 0.15 \\+ 3 & 0.1 \\\hline\end{array}$ ​ a. Construct a spreadsheet simulation model that computes the value of the stock profit in 3 months, 6 months, 9 months, and 12 months under the assumption that the change in profit over any 3-month period is independent of the change in profit over any other 3-month period. b. With the current profit of $20 per share, simulate the profit per share for the next four 3-month periods. What is the average profit in 12 months? What is the standard deviation of the profit in 12 months?

In a base-case scenario, the output is determined by assuming

A football tournament is conducted between Team-A and Team-B of a college and the winner being the first team to win four games of seven games. The probability that Team-A wins each game are as follows: Game 1 2 3 4 5 6 7 Probability of Win 0.48 0.5 0.45 0.6 0.55 0.40 0.55 ​ a. Set up a spreadsheet simulation model in which whether Team-A wins each game is a random variable. b. What is the probability that the Team- A win the tournament? c. What is the average number of games played regardless of winner?