The problem just described is beast approved by use of which quantitative method?
Answer(s): C
Two basic casts are involved in queuing waiting-line) models: 1) the cast of providing service including facility casts and operating casts), and 2) the cast of idle resources waiting in line. The latter may be a direct cast if paid employees are waiting, or an opportunity cast in the case of waiting customers. The objective of the queuing theory is to minimize the total cast of the system, including bath service and waiting casts, far a given rate of arrivals. This minimization occurs at the paint where the cast of waiting is balanced by the cast of providing service. A bank has two drive-in lanes to serve customers: one attached to the bank itself and one on an island. One teller serves bath stations. The bank is interested in determining the average waiting times of customers and has developed a model based on random numbers. The two key factors are the time between successive car arrivals and the time customers wait in line. Assume that the analysis begins with cars just arriving at bath service windows. bath requiring 3 minutes of service time. Car 1 is the attached window attached to the bank unless that window has more cars waiting than the island window. The lone teller will always serve the car that arrived first. If two cars arrive simultaneously, the one at the attached window will be served before the one at the island.
The techniques used in analyzing the problem is best described as:
Answer(s): A
Simulation is a technique for experimenting with logical/mathematical models using a computer. Despite the power of mathematics, many problems cannot be solved by known analytical methods because of the behavior of the variables and the complexity of their interactions. However, the performance of a quantitative model under uncertainty may be investigated by randomly selecting values for each of the variables in the model based on the probability distribution of each variable) and then calculating the value of the solution. If this process is performed a large number of times, the distribution of results from the model will be obtained. A bank has two drive-in lanes to serve customers: one attached to the bank itself and one on an island. One teller serves bath stations. The bank is interested in determining the average waiting times of customers and has developed a model based on random numbers. The two key factors are the time between successive car arrivals and the time customers wait in line. Assume that the analysis begins with cars just arriving at bath service windows. bath requiring 3 minutes of service time. Car 1 is the attached window attached to the bank unless that window has more cars waiting than the island window. The lone teller will always serve the car that arrived first. If two cars arrive simultaneously, the one at the attached window will be served before the one at the island.
The process of making sure that the model measures what it is supposed to measure is called:
Answer(s): D
Validation is a step in the simulation procedure. Some assurance is needed that the results of the experiment will be realistic. This assurance requires validation of the model -- often using historical data. If the model gives results equivalent to what actually happened, the model is historically valid. There is still some risk, however, that changes could make the model invalid for the future.
The marketing department of a company is deciding on the price to charge for a key product.In setting this price, marketing needs to consider the price that a major competitor will charge for a similar product because the competitor's price will affect the demand for the company's product. Similarly, in setting its price, the competitor will consider what the company will charge.What is an appropriate mathematical technique for analyzing such a decision?
Game or decision) theory is a mathematical approach to decision making when confronted with an enemy or competitor. Games are classified according to the number of players and the algebraic sum of the payoffs. In a two-person game, if the payoff is given by the loser to the winner, the algebraic sum is zero and the game is called a zero-sum game. If it is possible for both players to profit, however, the game is a positive-sum game. Mathematical models have been developed to select optimal strategies for certain simple games.
Because of the large number of factors that could affect the demand for its new product, interactions among these factors, and the probabilities associated with different values of these factors, the marketing department would like to develop a computerized model for projecting demand for this product. By using a random-number procedure to generate values for the different factors, it will be able to estimate the distribution of demand for this new product. This method of estimating the distribution of demand for the new product is called
Simulation is a technique in which a probabilistic process is first modeled. The inputs to the model are then varied a large number of times to estimate the distribution of possible outcomes from the model of the variable of interest. Simulations that use a random-number procedure to generate values for the inputs are referred to as Monte Carlo simulations.
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