To formulate a minimization problem for solution by the simplex method, we must add slack variables to a. only inequality constraints. b. only “less than” constraints. c. only “greater than” constraints. d. all inequality constraints.
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- A. What is the optimal solution and what is the optimal value of the objective function? B. Which constraints are binding? C. What are the dual values? Interpret each. D. If you could change the right-hand side of one constraint by one unit, which one would you choose? Why?Find solution using BigM (penalty) method.Maximize Z = x1 + 2x2 + 3x3 - x4subject to the constraintsx1 + 2x2 + 3x3 = 152x1 + x2 + 5x3 = 20x1 + 2x2 + x3 + x4 = 10and x1, x2, x3, x4 ≥ 01. 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 above
- Please do not give solution in image format thanku Consider the following set of constraints (Maximization problem): 10X+ 20y>= 43, and 30X+ 10Y >= 21.5. The following is true for this problem: a. Infeasible problem b. Unbounded problem c. X=0, Y=10 is the optimal solution d. X=10, Y=16 is the optimal solution. 2. Consider the following LP problem: Min 12X+ 12Y; Subject to ; 4 X + 4Y <= 31, and X + Y <= 93. Which one of the following is true: a. Optimal objective function value is O. b. Optimal objective function value is 93. c. Slack for each constraint is 0. d. X-46.5, Y=46.5 is the optimal solutionConsider the following LP problem: Min 6X+ 18Y; Subject to : 3 X + 9Y <= 47, and X + Y <= 141. Which one of the following is true?: a. Slack for each constraint is zero. b. Optimal Obj. function value is 94 c. X=70.5, Y=70.5 is the only optimal solution. d. Optimal Obj. function value is 0what is the dual equivalent and the final tableau of the given primal linear programming model?Min Y₀ = 10Y₁ + 8Y₂s.t.Y₁ + 2Y₂ ≥ 52Y₁ - Y₂ ≥ 12Y₁ + 3Y₂ ≥ 4Y₁ ≥ 0, Y₂ is unrestrictedprove or disprove the complementary slackness theorem.
- Which of the following is the converted constraint of 3x + 2y ≥ 35 under maximization of profit in simplex method? a. -3x +2y + S1 = -35 b. 3x +2y + S1 = 35 c. -3x -2y + S1 = -35 d. -3x -2y - S1 = -35 Which of the following is the converted constraint of 3x + 2y ≥ 35 under minimization of profit in simplex method? a. 3x + 2y - S1 + A1 = 35 b. 3x + 2y + S1 + A1 = 35 c. 3x + 2y + S1 - A1 = 35 d. 3x + 2y - S1 - A1 =-35 e. 3x + 2y - S1 + A1 =-3523. Consider the following constraints from a two-variable linear program: X ≥ 1; Y ≥ 1; X + Y ≤ 9. If these are the only constraints, which of the following points (X, Y) CANNOT be the optimal solution? Part 2 A. (1, 8) B. (8, 1) C. (4, 4) D. (1, 1) E. The question cannot be answered without knowing the objective function.Let Yi=1 if Xi positive; 0 otherwise, i=1-6.Which of the following statement regarding the production setup constraint is not true? Group of answer choices A. As long as M2 is larger than 400, it is large enough for the production setup constraint X2-M2Y2<=0 B. We use Xi-MiYi<=0 where Mi is large enough number to ensure when Xi is positive, Yi is 1. C. We can not use Xi-XiYi as the production setup constraint because it is nonlinear. D. The decision variable Yi represents whether or not to use machine i.
- In preparing a ≥ constraint for an initial simplex tableau, you would a. add a surplus variable. b. add slack variable. c. subtract an artificial variable. d. subtract a surplus variable and add an artificial variable.You are given the tableau shown in Table 74 for a maximization problem. Give conditions on the unknowns a1, a2, a3, b, and c that make the following statements true: a)The current solution is optimal. b)The current solution is optimal, and there are alternative optimal solutions. c)The LP is unbounded (in this part, assume that b 0).An XYZ company has a W, H, O plant with a monthly production capacity of 60 tons, 50 tons, and 42 tons, respectively; and has 3 sales warehouses in cities A, B, C, D Where each warehouse has a monthly requirement of 30 tons, 34 tons, 44 tons and 25 tons. With shipping cost W to ABCD = IDR 12,000,-, IDR. 8.000,-, Rp. 12.000,-, Rp. 14,000,-; H to A B C D = Rp. 8.000,-, Rp. 18.000,-, Rp. 10,000,-, Rp. 6.000,-; and O to ABCD = Rp. 16.000,-, Rp. 16.000,-, Rp. 2,000, Rp. 10,000,-. Please calculate using Vogel's Approximation Method or VAM Question a. What is the best transportation model in your opinion to solve the above problems? b. What is the minimum transportation cost to solve the shipping transportation problem! c. Based on these calculations, give suggestions regarding the transportation model and the amount of costs incurred by the company!