a. Maximize z = 66x₁22x2 Subject to Primal -X1 + X2 ≤-2 2x1 + 3x2 ≤ 5 X1, X2 ≥ 0 primal problems: Primal in Equation Form
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OPERRATION RESEARCH (UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. NO LONG EXPLANATION NEEDED.ANSWER IN 2 DECIMAL PLACES)
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- Determine whether the problem has multiple solutions, unbounded solutions, or no feasible solutions.Maximize z = 10x1 + 11x2 + 7x3, subject to 2x1 + 3x2 − 9x3 ≤ 72 2x1 + 5x2 − 10x3 ≥ 100 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0 The problem has multiple solutions. The problem has unbounded solutions. T he problem has no feasible solutions.b) Maximize Z = −40X1 −100X2s.t 10X1 + 5X2 ≤ 2502X1 + 5X2 ≤ 1002X1 + 3X2 ≤ 90X1, X2 ≥ 0Solve by simplex method, what are the solutions? Show that this problem hasmultiple solutions and find the solutions?Consider the following LP:Maximize z = 16x1 + 15x2subject to40x1 + 31x2 <=124-x1 + x2<= 1x1<=3x1, x2 >= 0(a) Solve the problem by the simplex method, where the entering variable is thenonbasic variable with the most negative z-row coefficient.
- Consider the following LP model in standard form, with a row for the objective function Z. a) Put it into Canonical form ( or Simplex Tableau form) with basic variables X1, X2 , and X3. b) Determine the association BFS (Basic Feasible Solution) and the new formula for the objective function Z Minimize 10X1 + 4X2 Sujbject to 3X1 + 2X2 - X3 = 60 7X1 + 2X2 - X4 = 84 3X1 + 6X2 -X5 = 72 X1, X2, X3 , X4 , X5 >= 0Consider the following problem: Minimize Z = 5X1 + 8X2 + 3X3 + 5X4 + 12X5 Subject to X1 + 3X2 + 5X3 + 6X4 + 3X5 > 60 and all variables are > 0, except X1 which is of unrestricted sign Use the Primal-Dual relations to solve both problems (i.e., the Primal and the Dual).Indetify the constraints that form the fesible region and identify the constraints that are rebundant. Equation: Maximize 5x1 + 3x2 Subjected to x1 + 5x2 ≤ 5 4x1 + 3x2 ≤ 12 x1 + x2 ≤ 4 x1 + x2 ≤ 5 5x1 + 7x2 ≤ 35 x1 + x2 ≥ 0
- Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 2), (0, 3), (2, 2), (2, 0), (1, 1), (2, 1), (3, 3)}. (a) Draw the directed graph of R. (b) Is R reflexive? Explain. (c) Is R symmetric? Explain. (d) Is R transitive? ExplainGiven four decision variables A, B, C, and D, which of the following could be a linear programming problem constraint? 1A + 2B - 1C/D >=23 1A + 2A*B + 3A*B/C + 4A*B*C*D >=100 1A + 2B + 3C + 4D >=100 1A + 2B/C + 3D <=45 1A + 2B*C + 3D <=100Find the optimal solution of the following LP models. Maximize z= 15x1+20x2 Subject to: x1+2x2 ≥ 10 2x1 - 3x2 ≤ 6 x1+x2 ≥ 6 x1,x2 ≥ 0
- 1. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the aboveTrue or False 1. Given three corner points A, B, and C of a linear programming problem, if A is adjacent to B and B is adjacent to C, then A can be determined from C by interchanging exactly two basic and two nonbasic variables. 2. For a set of primary and dual solutions to be feasible, the objective function value of the primary (Z) can never exceed that of the dual (W) no matter which problem is to maximize and which is to minimize. 3. If the current iteration is degenerate, the next iteration will also be degenerate. 4. The optimal (dual) primary solution can be obtained from the dual (primary) optimal tableau.We have 60 meters of fence and want to fence a triangular shaped area. Please formulate an NLP (do not try to solve) that will enable us to maximize the fenced area (Hint: The area of a triangle with sides of length a, b, and c is ( s (s – a) (s – b) (s – c))1/2, where s is half the parameter of the triangle).