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Problem 1. Describe the following terms (maximum of two lines for each term) Mathematical ModelsA mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Iconic modelsA model, considered from the point of view of its subject phenomena, beginning merely as an analog of the real mechanism that is supposedly unknown, can become, by a switch in the attitude of its users to its status, none other than a hypothetical mechanism Descriptive modelsDescriptive modeling is a mathematical process that describes real-world events and the relationships between factors responsible for them. The process is used by consumer-driven organizations to help them target their marketing and advertising efforts. Prescriptive modelsThe most advanced area of decision support on the analytics maturity spectrum. Prescriptive analytics provides the best outcomes for modeled situations based on the powerful concepts of optimization Optimization modelsEntails deciding how to best leverage limited assets, time and resources in situations with varying levels of uncertainty. Common prescriptive applications include determining budget usage, setting prices, managing a financial portfolio or running a business Deterministic modelsMathematical model in which outcomes are precisely determined through known relationships among states and events, without any room for random variation Stochastic modelsStochastic modeling is a technique of presenting data or predicting outcomes that takes into account a certain degree of randomness, or unpredictability Statistical modelsSimulation in which ranges of values for each variable (in the form of probability distribution) are used. In comparison, deterministic models use single estimates to represent the value of each variable. SimulationA model is a representation of an object, concept or system. A simulation shows the expected working of a system based on a model of the system. A model can be physical or abstract, and both types can be static or dynamic Systems analysisThe process of studying a procedure or business in order to identify its goals and purposes and create systems and procedures that will achieve them in an efficient wayProblem 2.Explain Rules of modeling and describe the following terms Decision variablesIdentify all decision variables by listing controllable parameters whose values can be controlled by decision maker, which affect functioning of system. Denote them by X_1,…..,X_n X = decision vector [■(X_1@.@X_2 )] = 〖(X_1,…..,X_n)〗^T ParametersThe proportionality assumptions and the addictively assumption must old for the objective function and all constant functions .Verify that all variable are continuous variables. Objective functionThe profit function if it is to be maximized or the cost function if it is to be minimized. ConstraintsIdentify all constraints and boundaries on decision variables. The constrains can be equality constraints: ġ_1(x) = b_i ,and inequality constraints: ġ_1(x) ≥ b_i orġ_1(x) ≤ b_i .The boundaries include lower or upper bound constraints on individual variables: X_j≥b_j or X_j≤b_j ,and the non-negativity restriction : X_j≥ 0
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