stands can sell both inside the stadium. Then, she had a great idea, she thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell. A. Formulate a linear programming model for this case X1= the number of slices of pizza X2=the number of hot dog X3=the number of sandwiches The objective is to maximize total profit. Profit is calculated for each variable by subtracting cost from the selling
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Solutions to Linear Programming Problems Applied Statistics and Quantitative Method Assignment #1 GROUP 6 Abie Widyatmojo Billy Biondi Donny M Sitompul R Nurjaman B Vincentius Ricky T 1306355990 1306456261 1306356412 1306357270 1306420466 Problem #1 : Serendipity Introduction The three princes of Serendip went on a little trip. They could not carry too much weight. More than 300 pounds made them hesitate. They planned to the ounce. When they returned to Ceylon they discovered that their
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Chapter 1 Linear Programming 1.1 Transportation of Commodities We consider a market consisting of a certain number of providers and demanders of a commodity and a network of routes between the providers and the demanders along which the commodity can be shipped from the providers to the demanders. In particular, we assume that the transportation network is given by a set A of arcs, where (i, j) ∈ A means that there exists a route connecting the provider i and the demander j. We denote by cij the
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Preventive Maintenance and Replacement Scheduling: Models and Algorithms By Kamran S. Moghaddam B.S., University of Tehran, 2001 M.S., Tehran Polytechnic, 2003 A Dissertation Proposal Submitted to the Faculty of the Graduate School of the University of Louisville in Partial Fulfillment of the Requirements for the Doctor of Philosophy Candidacy Department of Industrial Engineering University of Louisville Louisville, Kentucky, USA November 2008 ©Copyright 2008 by Kamran S. Moghaddam
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are the most popular food items among fans and so these are the items she would sell. If Julia clears at least $1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth. A. Formulate a linear programming model for this case. Decision Variables Representing “x1” as pizza slices, “x2” as hot dogs, and “x3” as barbeque sandwich The Objective Function The objective is to maximize total profit. Profit is calculated for each variable by
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assembly line, machine hours availability and requirement for completing various manufacturing jobs, standard product costs for each model and the overhead budget for 2012. Method: For finding the product mix that maximizes contribution a linear programming model was prepared using, maximize monthly contribution as the objective function, number of model 101 trucks and number of model 102 trucks as the decision variables, the analysis was bound to the constraints of requirement and availability
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RESEARCH “PENGEMBANGAN METODE TRANSPORTASI DALAM OPERASI PENELITIAN” TYPE II – COMPARE & CONTRAST IQBAL TAWAKKAL - 1506694736 PROGRAM MAGISTER TEKNIK INDUSTRI - SALEMBA UNIVERSITAS INDONESIA 1. INTRODUCTION A special class of linear programming problem is Transportation Problem, where the objective is to minimize the cost of distributing a product from a number of sources (e.g. factories) to a number of destinations (e.g. warehouses) while satisfying both the supply limits and the
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Answer 1 a. We have to make a decision, how much space should we lease and for how long. Constraint is the minimum space required. The objective of this function is to minimize b. Decision Variables: Let Xij = the space leased in month (i) for the period of (j) months, for i = 1, 2, …, 5 and j = 1, …, 6. Objective Function: Minimize Z = 65(X11 + X21 + X31 + X41 + X51) + (100X12 + X22 + X32 + X42) + 135(X13 + X23 + X33) +160(X14 + X24) + 190X15 Constraints: X11 + X12 + X13 +
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25 3.3. CUTTING PLANE METHODS Consider a pure integer linear programming problem in which all parameters are integer. This can be accomplished by multipying the constraint by a suitable constant. Because of this assumption, also the objective function value and all the "slack" variables of the problem must have integer values. We start by solving the LP-relaxation to get a lower bound for the minimum objective value. We assume the final simplex tableau is given, the basic variables having columns
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Solutions 56:171 Operations Research Homework #3 Solutions – Fall 2002 1. Revised Simplex Method Consider the LP problem Maximize subject to z = 3 x1 − x2 + 2 x3 x1 + x2 + x3 ≤ 15 2 x1 − x2 + x3 ≤ 2 − x1 + x2 + x3 ≤ 4 x j ≥ 0, j = 1, 2,3 a. Let x4 , x5 , &, x6 denote the slack variables for the three constraints, and write the LP with equality constraints. Answer: Maximize z = 3 x1 − x2 + 2 x3 subject to x1 + x2 + x3 + x4 = 15 2 x1 − x2 + x3 + x5 = 2 − x1 + x2 + x3 + x6 = 4 x j ≥ 0, j = 1, 2,3, 4
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