For the Big-M tableau (of a minimization LP and row0 at bottom), Z 0 0 0 perform the simplex algorithm to find the optimal tableau. x1 6 2.1 4 -2010 Z X2 2.1 4.1 12 -1500 I1 5 e1 e2 e3 -1 0 0 0 -1 0 0 0 -1 0 0 0 a1 1 0 0 -100 x2 e1 e2 e3 a1 । a2 0 1 0 -100 a2 a3 a3 RHS 0 8 0 1 -100 RHS 12 24 0
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- Use the simplex algorithm to solve the following linear optimisation problem: maximisef(x1,x2,x3)=3x1+x2+2x3 subjectto: 3x1 +2x2 +x3 ≤8 x1 +2x2 +2x3 ≤4, x1,x2,x3 ≥0. You must address each of the 5 steps of the algorithm as presented in the course notes and videos in your answer.When using the simplex algorithm, an error was made in choosing the pivot row. Which of the following will be the result of this? The solution in the next tableau will: a. have a worse objective value b. be nonbasic c. be infeasible d. be unaffectedSolve the following linear optimization model using the Simplex Algorithm:Maximize z(x1, x2) = 3x1 + 2x2Subject to2x1 + 2x2 ≤ 82x1 + 1x2 ≤ 6x1, x2 ≥ 0
- Consider the following LP:min 5x1 + 4x2s.t. x1 + x2 ≥ 12x1 − x2 ≥ 13x2 ≤ 2x1, x2 ≥ 0.a. Write down the dual of this LP.b. We know that by strong duality, we can either solve this LP or its dual form to get the sameoptimal objective value. If you apply the simplex algorithm, which one would you rathersolve? Make your choice and apply the simplex algorithm to solve it.Consider the following LP:min 5x1 + 4x2s.t. x1 + x2 ≥ 12x1 − x2 ≥ 13x2 ≤ 2x1, x2 ≥ 0.1. Write down the dual of this LP.2. We know that by strong duality, we can either solve this LP or its dual form to get the sameoptimal objective value. If you apply the simplex algorithm, which one would you rathersolve? Make your choice and apply the simplex algorithm to solve it.construct the initial plus one simplex tableaux for the following LPP: Max Z = X1 + 2x2 + 4x3 st : X1+X2 + X3 ≤ 400 x2+2x3 ≤ 300 x1 + x2 ≤ 200 x1, x2, x3 ≥ 0
- The owner of the Consolidated Machine Shop has $10,000 available to purchase a lathe, a press, a grinder, or some combination thereof. The following 0–1 integer linear programming model has been developed to determine which of the three machines (lathe, x1, press, x2, or grinder, x3) should be purchased in order to maximize annual profit: Maximize Z = 1000x1 + 700x2 + 800x3 (profit, $) subject to: $5,000x1 + 6,000x2 + 4,000x3 ≤ 10,000 (cost, $) x1 , x2 , x3 = 0 or 1 1. Solve this model by using the computer.Use Simplex Algorithm to determine the optimal solution of this LP problem. Maximize z = 2x1 − x2 + 2x3subject to:2x1 + x2 ≤ 10x1 + 2x2 − 2x3 ≤ 20x2 + 2x3 ≤ 5x1, x2, x3 ≥ 0a) is your colleague correct in their assertion? if not, how would you explain to them why this tableau does not offer the optimal solution? b) if this tableau yields the optimal solution, what is it? if not, identify the next pivot element according to the simplex algorithm
- Use the simplex algorithm to solve the following problem (Use tableaus)First 3 parts are solved. 5-28 Consider the linear programmax x1 + x2s.t. x1 + x2 ≤ 9-2x1 + x2 ≤ 0x1 - 2x2 ≤ 0x1, x2 ≥ 0(a) Solve the problem graphically.(b) Add slacks x3,c, x5 to place the modelin standard form.(c) Apply rudimentary simplex Algorithm 5Ato compute an optimal solution to yourstandard form starting with all slacks basic.(d) Plot your progress in part (c) on thegraph of part (a).(e) How can the algorithm be making progress when l = 0 if some moves of part(c) left the solution unchanged? Explain.5-29 Do Exercise 5-28 for the LPmax x1s.t. 6x1 + 3x2 ≤ 1812x1 - 3x2 ≤ 0x1, x2 ≥ 0Recreate the LINEAR PROGRAMMING PROBLEM based on the image of the LP MODEL attached below