TUTORIAL 2 Linear Programming - Minimisation Special cases Simplex maximisation 1. Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s needs. For a new client‚ Innis has been authorised to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs
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20 CHAPTER 3 NEW ALTERNATE METHODS OF TRANSPORTATION PROBLEM 3.1 Introduction The transportation problem and cycle canceling methods are classical in optimization. The usual attributions are to the 1940’s and later. However‚ Tolsto (1930) was a pioneer in operations research and hence wrote a book on transportation planning which was published by the National Commissariat of Transportation of the Soviet Union‚ an article called Methods of ending the minimal total kilometrage in cargo-transportation
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DCO21020 Operations Research Lecture 2 TAHA Example 2.1-1 (Page 47) : The Reddy Mikks Company The Reddy Mikks Company produces both interior and exterior paints from two raw materials‚ M1 and M2. Tons of raw material per ton of Maximum daily availability Exterior Paint Interior Paint (tons) Raw material M1 Raw material M2 Profit per ton ($1000s) 6 1 5 4 2 4 24 6 A market survey indicates that the daily demand for interior paint cannot exceed that for exterior paint by more than 1 ton. Also
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Pace University DigitalCommons@Pace Faculty Working Papers Lubin School of Business 11-1-1999 The Mystery of Linear Programming Explained: Second Edition Jack Yurkiewicz Pace University Follow this and additional works at: http://digitalcommons.pace.edu/lubinfaculty_workingpapers Recommended Citation Yurkiewicz‚ Jack‚ "The Mystery of Linear Programming Explained: Second Edition" (1999). Faculty Working Papers. Paper 21. http://digitalcommons.pace.edu/lubinfaculty_workingpapers/21
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Program in Scientific Computing and Computational Mathematics‚ Stanford University‚ Stanford‚ CA‚ 2008. [20] A. Majthay. Optimality conditions for quadratic programming. Math. Programming‚ 1:359–365‚ 1971. [21] J. Nocedal and S. J. Wright. Numerical Optimization. Springer-Verlag‚ New York‚ 1999. [22] P. M. Pardalos and G. Schnitger. Checking local optimality in constrained quadratic programming is NP-hard. Oper. Res. Lett.‚ 7(1):33–35‚ 1988. [23] P. M. Pardalos and S. A. Vavasis. Quadratic programming
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Stock Rationing in a Make-to-Stock Production System with Two Demand Classes and Service Level Constraint [pic] This paper studies the stock rationing problem of a single-item make-to-stock production system with two demand classes and lost sale. There are service level requirements for both demand classes. Demands follow Poisson distributions‚ and production time is exponentially distributed. We derive the condition of the existence of a feasible rationing policy of the problem first. Then the
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Z00_REND1011_11_SE_MOD7 PP2.QXD 2/21/11 12:39 PM Page 1 7 MODULE Linear Programming: The Simplex Method LEARNING OBJECTIVES After completing this chapter‚ students will be able to: 1. Convert LP constraints to equalities with slack‚ surplus‚ and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3. Interpret the meaning of every number in a simplex tableau. 4. Recognize special cases such as infeasibility‚ unboundedness and degeneracy. 5
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military operations. In essence you can state that OR is a technique that helps achieve best (optimum) results under the given set of limited resources. Over the years‚ OR has been adapted and used very much in the manufacturing sector towards optimization of resources. That is to use minimum resources to achieve maximum output or profit or revenue. Learning Objectives The learning objectives in this unit are 1. To formulate a Linear programming problem (LPP) from set of statements. 2. To solve
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its resources (Jacobs & Chase‚ 2013). In this case the resources are time‚ money‚ and employees. In order to provide Mr. Rodriguez with the information he requested‚ linear programming will be utilized. Linear programming is the “several related mathematical techniques used to allocate limited resources among competing demands in an optimal way” (Jacobs & Chase‚ 2013‚ appendix
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BSTA 450 - Review Sheet - Test 2 1. Consider the following linear programming problem: Maximize Z = 400 x + 100y Subject to 8 x + 10y ≤ 80 2 x + 6y ≤ 36 x≤ 6 x‚ y ≥ 0 BSTA 450 Find the optimal solution using the graphical method (use graph paper). Identify the feasible region and the optimal solution on the graph. How much is the maximum profit? Consider the following linear programming problem: Minimize Z = 3 x + 5 y (cost‚ $) subject to 10 x + 2 y ≥ 20 6 x + 6 y ≥ 36 y ≥ 2 x‚ y ≥ 0 Find
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