• Integer Programming
    x7 x6 2x6 x4 1 1 2 0 12.7-9. Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve the following MIP problem interactively. Maximize Z 3x1 4x2 2x3 x4 2x5, subject to 2x1 x1 2x1 and xj 0, for j 1, 2, 3, 4, 5 xj is binary, for j 1, 2, 3. D,I x2 3x2 x2 x3 x3 x3 x4 x4 x4...
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  • Linear Programming
    Company’s product mix problem as follows, using linear programming: Maximize profit = $7X1 + $5X2 subject to LP constraints: 2 X1 + 1X2 ≤ 100 4 X1 + 3 X2 ≤ 240 where X1 equals the number of Walkmans produced and X2 equals the number of Watch-TVs produced. To convert these inequality constraints to...
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  • Operation Reasearch
    tables and no chairs to get the max profit. 3.4 Special Cases in Graphical Method 3.4.1 Multiple Optimal Solution Example 1 Solve by using graphical method Max Z = 4x1 + 3x2 Subject to 4x1+ 3x2 ≤ 24 x1 ≤ 4.5 x2 ≤ 6 x1 ≥ 0 , x2 ≥ 0 Solution The first constraint 4x1+ 3x2 ≤ 24, written in a...
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  • Industrial Engineering
    assignment problem can be stated as: Minimize (maximize): Z= Subject to: ij Xij for j= 1,2,………, m for i= 1,2,………, n Xij = 0 or 1 for al i and j The following is a step by step algorithm that uses the Hungarian method to solve the general assignment problem. Step 1: for the original...
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  • Co250
    7 z=57 Fractional x3 9 x3 10 z=42 Fractional z=49 Fractional infeasible z=49 Fractional x8 2 x8 3 x5 0 x5 z=46 Integer 1 z=45 Fractional z=42 Integer z=46 Fractional 2. Use branch and bound to solve the following linear program, max subject to...
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  • Mcaw Www
    first LP problem is max z = 4x1 + 5x2 subject to x1 + x2 ≤5 6x1 + 10x2 ≤45 x2 ≤3. 17 / 80 Choice of way to split The second LP problem is given by max z = 4x1 + 5x2 subject to x1 + x2 ≤5 6x1 + 10x2 ≤45 x2 ≥4. 18 / 80 Bounds on the optimal value and adding branches 1. If the...
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  • Essay
    represent the amount of an unused resource. We formulate the Shader Electronics Company’s product mix problem as follows, using linear programming: Maximize profit Subject to LP constraints: 2X1 4X1 1X2 3X2 100 240 $7X1 $5X2 where X1 equals the number of Walkmans produced and X2 equals the number of...
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  • Tora Software
    (100, 0). Therefore, the values of x1 and x2 are 100 and 0 respectively. Maximum Profit, Zmax = 4x1 + 2x2                                  = 4(100) + 2(0)                                  = Rs. 400.00 Example 10: Solve the following LPP by graphical method. Minimize Z = 18x1+ 12x2 Subject to...
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  • Business Communicaton
    recorded, it is optimum, or else no integer valued feasible solution exists. Solved Problem 2 Use branch and bound technique to solve the following IPP Maximise z = 7x1 + 9x2 ---------------- (1) Subject to the constraints – x 1 + 3x2 < 6 -–------------ (2) 7x1 + x2 < 35 0 < x1, x2 < 7...
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  • Statistics
    , equivalently, z , x1 , x2 = 0: Putting this equation together with the constraints, we get the following system of linear equations. = 0 z ,x1 ,x2 2x1 +x2 +x3 = 4 x1 +2x2 +x4 = 3 Row 0 Row 1 Row 2 7.1 7.2. SOLUTION OF LINEAR PROGRAMS BY THE SIMPLEX METHOD 89 Our goal is to maximize z...
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  • Lp Free Chapter 6 Tmh
    optimality d. Range for multiple changes PROBLEMS 1. Solve these problems using graphical method and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables. a. Maximize Z 4x1 3x2 Subject to 4x2 48 kg Material 6x1 8x2 80 hr Labour 4x1 x1...
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  • Introduction to Operation Research Hillier and Liberman
    based on the simplex method to solve the problem. 4.6-15.* Consider the following problem. Maximize Z x1 4x2, subject to x2 6 3x1 x1 2x2 4 x1 2x2 3 (no lower bound constraint for x1). (a) Solve this problem graphically. (b) Reformulate this problem so that it has only two functional...
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  • Marketing Management
    following in equations: 4 x1 + 2 x 2 ≤ 10 8 2 x1 + x 2 ≤ 8 3 x2 ≤ 6 x1, x 2 ≥ 0 Formulate & solve the LP problem by using graphical method so as to optimize both P1 & P2. Solution Objective: Maximise Z = 4 x1 + 3 x2 Since the origin (0,0) satisfies each and every constraint, all points below the...
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  • Simplex Method
    M7-1 Convert the following constraints and objective function into the proper form for use in the simplex method: Minimize cost = 4X1 + 1X2 subject to 3X1 + X2 = 3 4X1 + 3X2 Ú 6 X1 + 2X2 … 3 SOLVED PROBLEMS M7-41 Solution Minimize cost = 4X1 + 1X2 + 0S1 + 0S2 + MA 1 + MA 2 subject to...
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  • Ch 9 solutions
    artificial variables) and 3 constraints. b. The dual would have 2 constraints and 5 variables (3 decision variables and 2 slack variables). c. The dual problem would be smaller and easier to solve. maximize profit ϭ 0.5X1 ϩ 0.4X2 primal constraints: 2X1 ϩ 1X2 р 120 2X1 ϩ 3X2 р 240 X1, X2 у 0...
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  • Linear Program
    values of (x1, x2) are estimated to be those given in the following table: 3.4-3. Use the graphical method to solve this problem: Maximize Z 15x1 20x2, subject to x1 2x1 x1 and x1 D 2x2 3x2 x2 10 6 6 0, x2 0. 3.4-4. Use the graphical method to solve this problem: Minimize Z...
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  • Linear Programming
    subject to 3X1 + 1X2 + 1A 1 = 3 4X1 + 3X2 - 1S1 1X1 + 2X2 + 1A 2 = 6 + 1S2 = 3 Solved Problem M7-2 Solve the following LP problem: Maximize profit = $9X1 + $7X2 subject to 2X1 + 1X2 … 40 X1 + 3X2 … 30 Solution We begin by adding slack variables and converting inequalities into...
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  • Quanti
    be sold for a $15 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach. Let X1 = the number of air conditioners scheduled to be produced X2 = the number...
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  • Quantitative-Techniques-for-Management
    graphically: Maximize Z = 8x1 + 10x2 Subject to constraints, 2x1 + 3x2 ³ 20 4x1 + 2x2 ³ 25 where 11. x1 , x2 ³ 0 Solve the two variable constraints using graphical method. Maximize Z = 50x1 + 40x2 Subject to constraints x1 ³ 20 x2 £ 25 2x1 + x2 £ 60 where x1 , x2 ³ 0 12. Solve the following LP...
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  • Abcdefghijklmnopqrstuvwxyz
    5 = 20 Marks Answer all Questions : 1. Use Branch and Bound method to solve the following LPP. Maximize z = gx1 + gx2 Subject to the constraints - x1 + 3x2 ≤ 6 7x1 + 40 x2 ≤ 35 x2 ≤ 7 x1 , x2 ≥ 0 and integers 2. A manufacturing company produces two products A and B. The time requirement...
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