An audit manager has just returned from an executive training program and has suggested that the audit department develop a mathematical model to help identify factors that may be causing changes in the cost of production. According to the manager, the model should recognize that the company currently has three separate production (cost) centers.Which of the following approaches would best provide the analysis suggested by the audit manager?
Answer(s): C
Regression analysis extends correlation to find an equation for the linear relationship among variables. The behavior of a dependent variable, such as cost of production, is explained in terms of one or more independent variables (for example, raw material costs, employees, overtime). Thus, multiple regression analysis determines functional relationships among quantitative variables.
A bank has two drive-in lanes to serve customers:The technique used in analyzing the problem is best described as:
Answer(s): A
Answer A is correct. 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: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:
Simulations that use a random-number procedure to generate values for the inputs are Monte Carlo simulations.
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