2.SOLVE USING BIG-M METHOD Maximize 3x1 - x₂ subject to x1 - x₂ ≤ 3 2x1 ≤ x₂ x₁ + x₂ > 12 X1, X2 ≥0
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- For the products A, B, C, and D, which of the following could be a linear programming objective function? Select one: a. Z = 1A + 2BC + 3D b. Z = 1A + 2AB + 3ABC + 4ABCD c. Z = 1A + 2B + 3C + 4D d. Z = 1A + 2B/C + 3DUse the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 + 4x2 < 34 x1 > 0, x2 > 0 x1 = x2 = x3 =Solve by the Big M – method: Maximize Ζ= x1 + 2x2 −3x3 + x4 Subject to x1 +2x2 +3x3 =15 2x1 +x2 + 5x3 = 20 x1 +2x2 +x3 +x4 = 10 x1 + 4x2 +6x3 ≤ 5 Where x x x x1, 2, 3, 4 ≥ 0
- 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.Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.Find 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
- Find the values of x1 and x2 where the following two constraints intersect. (Round your answers to 3 decimal places.) (1) 10x1 + 5x2 ≥ 50 (2) 1x1 + 2x2 ≥ 12Simplex Method Solve the following LP problem using the simplex method. Maximize: P = 9x + 7ySubject to:2x + y ≤ 40x + 3y ≤ 30x, y ≥ 0 What is the entering variable and leaving variable in Table 2? a. Entering Variable: x and Leaving Variable: S2 b. Entering Variable: y and Leaving Variable: S2 c. Entering Variable: y and Leaving Variable: S1 d. Entering Variable: x and Leaving Variable: S1Consider the given LP:Maximize z = 4x1 + 6x2 + 8x3Subject to 3x1 + 2x2 + 5x3<= 30 9x1 + 2x2 + 7x3 <= 126 2x1 + 3x2 + x3<= 60 xi>= 01-Find the optimal values of Z, x1, x2, x3 by using the simplex method.3-If the RHS of the constraint 1 is 34 instead of 30, what is the new value of Z?
- Solve using the simplex method (Use Excel Solver) Maximize P = 6 x1 + 3x2 subject to -2 x + 3x <= 9 -x1 + 3x2 <= 12 x1, x2 >=0Example 1. The Big M Method solve LP with mixed constraints Minimize: Z = 4x1 + 2x2 + x3 Subject to: 2x1 + 3x2 + 4x3 ≤ 14 3x1 + x2 + 5x3 ≥ 4 x1 + 4x2 + 3x3 ≥ 6 x1, x2, x3≥ 0Solve using Simplex MethodMaximize z = 4x1 + 3x2subject to-x1 +2x2 ≤43x1 +2x2 ≤14x1 – x2 ≤ 3x1, x2 ≥ 0