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- 4. Solve the following LP problem using the simplex algorithm for maximum tableaus: Maximize: f(x1, x2, 3) = 1 + 2x2 + 2x3 subject to ₁+ 2x2 + 2x3 ≤ -4 2x1 + 3x3 ≤ 5 2x1x2 + x3-4 X1, X2, X3 20Use 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 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 problem using the tableau implementation of the simplex algorithm. minimize - 6x - 4x2 + 2x3 subject to x, + x2 + 4x3 < 20 - 5x2 + 5x3 < 100 X1 + 3x2 + x3 s 400 *1 20 *3 204. Consider the following LP: max z = 6x1 + x2 X1 + x2 5 5 2x, + x2 < 6 st. X1,x2 2 0 (a) Solve this problem using the Simplex Algorithm and obtain the optimal tableau for this problem. (b) If we add a new variable x3 such that: max z = 6x1 + x2 + x3 X1 + x2 + ax3 S 5 2x, + x2 + bx356 X1, X2, X3 20 where a and b are scalar values, define the conditions under which the current basis stay st. optimal.. Use the simplex algorithm to solve the following linear optimisation problem: maximise f(x1, x2, x3) = 3x1 + x2+ 2x3 subject to: Зх1 + 2л2 + з 0.
- 2. Apply the first phase of the 2-phase simplex algorithm to the following linear pro- gramme giving the initial tableau and each further tableau produced. Give the starting tableau for the second phase if there is one. maximize 2x1 x23x3 subject to X2 - x3 ≤ 2, x13x2+2x3 ≥ 3, 2x12x2 x3 = 4, x1, x2, x3 0.Use the simplex algorithm to solve the following linear optimisation problem: maximise f(x1, x2, x3) = 3x1+ x2 + 2x3 subject to: 3x1 + 2x2 + x3 0. You must address each of the 5 steps of the algorithm as presented in the course notes and videos in your answer.Consider the linear program max 10x – y s.t. -5x + 3y < 15 Зх — 5у <8 х, у 2 0 Use the simplex method to show that the problem is unbounded. (Show each iteration of the algorithm in the solution.)
- Solve the following linear programs (LPs) using the simplex algorithm. • For each tableau you obtain, write the associated BFS and its objective value. • For each LP, find the complete optimal solution set and write it using appropriate mathematical notation. Use only the information in the tableaux to justify your answer. minimize z(x1, x2) subject to -x1 X2 + x2 0Apply the first phase of the 2-phase simplex algorithm to the following linear pro- gramme giving the initial tableau and each further tableau produced. Give the starting tableau for the second phase if there is one. maximize 2x1 + x2+3x3 subject to x2-x32, 1+3x2+2x3 ≥ 3, 2x1 +22+3 = 4, x1, x2, x3 0.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