In order to understand this topic‚ continuous-time system comes into different classifications which are the following: * Linear and Nonlinear Systems A system is linear if it follows the superposition principle. Also‚ it satisfies the additivity and homogeneity properties. Hence‚ if a system does not satisfy either of the two properties‚ it is said to be a non-linear system. * Time-varying and Time-Invariant Systems A system is said to be
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Solver is a tool to model and solve linear and nonlinear programming problems. To access it‚ open Excel‚ choose the tab “Data” and select “Solver” from the “Analysis” group. If it is not there‚ you have to install it‚ by clicking the “File” tab (or the Office button)‚ then “Options”‚ then “Add-Ins”‚ and then “Manage Add-Ins”. Check “Solver” there. To solve the model‚ you have to first program in on a spreadsheet. In the attached “excel-example.xls” we solve the linear programming problem max 3x1 + 2x2
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the following demand data for the past 8 months: Month Demand for Soft Shag Carpet (1‚000 yd.) 1 8 2 12 3 7 4 9 5 15 6 11 7 10 8 12 a. Compute a 3-month moving average forecast for months 4 through 9. b. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of 0.55‚0.33‚and 0.12 to the months in sequence‚ starting with the most recent month. c. Compare the two forecasts by using MAD. Which forecast appears to be
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Algebra I Chapter 5 Study Guide Writing Linear Equations Name ________________ Due: Tuesday‚ January 17 (Exam week) 100 points Writing Linear Equations in a Variety of Forms Using given information about a __________‚ you can write an ________________of the line in _____________ different forms. Complete the chart: Form (Name) Equation • • Important information The slope of the line is ____. The __ - ___________ of the line is _____. The slope of the line is _____. The line
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Integer Programming 9 The linear-programming models that have been discussed thus far all have been continuous‚ in the sense that decision variables are allowed to be fractional. Often this is a realistic assumption. For instance‚ we might 3 easily produce 102 4 gallons of a divisible good such as wine. It also might be reasonable to accept a solution 1 giving an hourly production of automobiles at 58 2 if the model were based upon average hourly production‚ and the production had the interpretation
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16 15 13 16 14 6 20 100 MARKS RECEIVED 1 Question 1 Graphical solution (16 marks) For a linear programming model given below: Decision variables x1 Units of product 1 to produce. x2 – Units of product 2 to produce. Objective function Maximize 4.0x1 + 3.6x2 Constraints Constraint 1: 11x1 + 5x2 > 55 Constraint 2: 3x1 + 4x2 < 36 Constraint 3: 4x1 – 9x2 < 0 Nonnegativity: x1‚ x2 >= 0 Solve this linear programming model by using the graphical approach (Graph paper is provided on the next page)
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Question 2 .2 out of 2 points Correct Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Answer Selected Answer: True Correct Answer: True Question 3 .2 out of 2 points Correct Surplus variables are only associated with minimization problems. Answer Selected Answer: False Correct Answer: False Question 4 .2 out of 2 points Correct In a linear programming problem‚ all model parameters are assumed to be known
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Operations Management: Processes and Supply Chains‚ 10e (Krajewski et al.) Chapter 14 Forecasting 1) The repeated observations of demand for a product or service in their order of occurrence form a pattern known as a time series. Answer: TRUE Reference: Demand Patterns Difficulty: Easy Keywords: time series‚ repeated observations 2) One of the basic time series patterns is random. Answer: TRUE Reference: Demand Patterns Difficulty: Easy Keywords: time series‚ pattern‚ random
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Math Exam Notes Unit 1 The Method of Substitution -Solving a linear system by substituting for one variable from one equation into the other equation -To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step
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of the functional notation f(x) 1.4 Determine the value of f(x) given a value for x B. Linear Functions 1. Demonstrate knowledge and skill related to linear functions and apply in solving problems 1. Define the linear function f(x) = mx + b 2. Given a linear function Ax + By = C‚ rewrite in the form f(x) = mx + b and vice versa 3. Draw the graph of a linear function given the following: * any two points *
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