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- Use the simplex method to solve. Maximize z = 4x1 + 2x2, subject to 3x1 + x2 < 22 3x1 + 4x2 < 34 x1 > 0, x2 > 0 x1 = x2 = x3 =Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize f = 8x + 9y + 3z subject to 2x + 7y + 8z ≤ 100 6x + 3y + z ≤ 160 3x + 4y + 9z ≤ 10 .Solve using the simplex method (Use Excel Solver) Maximize P = 6 x1 + 3x2 subject to -2 x + 3x <= 9 -x1 + 3x2 <= 12 x1, x2 >=0
- Analyze algebraically what special case in simplex application is present in each of the LP model below. Give an explanation to support your answer. a) Maximize z = 4x1 + 2x2 Subject to: 2x1 - x2 ≤ 2 3x1 - 4x2 ≤ 8 x1, x2 ≥ 0b) Maximize z = 3x1 + 2x2 Subject to: 4x1 - x2 ≤ 8 4x1 + 3x2 ≤ 12 4x1 + x2 ≤ 8 x1, x2 ≥ 0Solve Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0 Use simplex method.Please help with correct answers in details: step by step Q1 The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 3x1 + x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) ______ to ______? Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) _______ to _______? Compute the dual value for the first constraint. _______ Compute the dual value for the second constraint. _______ Compute the dual value for the third constraint. _______
- a. Maximize Z = 6X1 + 18X2+20X3 (Don't use excel shortcut solve manually by Simplex LPP method)Sub toX1 + X2 +X3 = 6010X1 +15X2 +20X3 = 9002X1 + 3X2 +3X3≤100And X1, X2, X3 >=0For 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 + 3DMax Z = 6X1 + 18X2+20X3 Sub to X1 + X2 +X3 = 60 10X1 +15X2 +20X3 = 900 2X1 + 3X2 +3X3≤100 And X1, X2, X3 >=0 (SOLVE MANUALLY USING SIMPLEX METHOD PLEASE DON'T USE SHORTCUTS)
- Given the following LP: Min 4x1 + 6x2 s.t 2x1 + 2x2 ≥ 3, x1 + 3x2 ≥ 2, x1 + 3x2 ≥ 0, Find its dual LP. Use graphical method or the Simplex algorithm, solve the primal LP in (1). Use graphical method or the Simplex algorithm, solve the dual LP (that you find in Part A). Find its dual LP.Consider the following all-integer linear program:max 5x1 + 8x2s.t. 9x1 + 4x2 ≤ 361x1 + 2x2 ≤ 10x1, x2 ≥ 0 and integer.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