Consider the following IP. The optimal tableau for this IPs linear programming relaxation is also given in the table below. Use the cutting plane algorithm to find the optimal solution. Z 1 OC 0 X₁ 0 1 0 max z = 2x₁ - 4x2 s.t. 2x1 + x₂ = 5 -4x₁ + 4x₂ ≤ 5 X1, X₂ = 0; x1, x₂ integer X₂ 0 0 $₁ د بن سدان است $2 6 12 rhs MAINTE 15
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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.Use the simplex algorithm to find the optimal solution to the following LP: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 ≥ 0
- Solve the following linear optimization model using the Simplex Algorithm:Maximize z(x1, x2) = 3x1 + 2x2Subject to2x1 + 2x2 ≤ 82x1 + 1x2 ≤ 6x1, x2 ≥ 0The 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.Please do not give solution in image format thanku QUESTION: Find the optimal integer solution of the integer programming problem given below with the 'cut plane algorithm' and draw the tree diagram. Max.z = 3x1 + 5x2 şkg 3x1 + 4x2 ≤ 25 x1 + 4x2 ≤ 16 x1 + x2 ≤ 8 x1 , x2 ≥ 0 and integer
- Solve the following mixed integer programming problem by using Branch and Bound algorithm. Maximize Z = x1 +x2 Subjected to 2x1 + 5x2 ≤ 1 6x1+ 5x2 ≤ 30 x2 ≥ 0 x1 ≥ 0 and integers.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 unaffected22) Determine using the Simplex algorithm the optimal solution to the following linear programming problem:
- An advertising firm has D dollars to spend on reachingcustomers in T separate markets. Market t consists of ktpeople. If x dollars are spent on advertising in market t, theprobability that a given person in market t will be reachedis pt(x). Each person in market t who is reached will buy ctunits of the product. A person who is not reached will notbuy any of the product. Formulate a dynamic programmingrecursion that could be used to maximize the expectednumber of units sold in T markets..A linear programming problem has objective function P = 3x+2y and the following linear inequality constraints below. How many slack variables are needed for the simplex algorithm? What is the correct way to arrange this equation in order to enter it into a Simplex Tableau?Consider the following linear programming problem Minimize Z=5X1+6X2+3X3 Subject to 5x1+5x2+3x3>=50 x1+x2-x3=20 7X1+6X2-9X3>=30 5x1+5x2+5x3>=35 2x1+4x2-15x3>=10 12x1+10x2>=90 x2-10x3>=20 X1, X2, X3 >=0 In an Excel workbook, solve the problem by using the Solver. Generate the Solver sensitivity and answer reports. In this Word document, write the mathematical formulation of the dual problem. Generate a sensitivity report of the dual problem. Solve the dual problem in another sheet of the same Excel file. In this Word document, describe whether the solution of the dual problem offers a computational advantage and explain why. Submit the Excel workbook as a separate attachment.