Consider the LP with n variables and 2n linear constraints, henceforth de- noted CUBER: max S = xn -10x1 10x1 ≤ 9 -1 - xi 10x+1 ≤ 0 i = 1,...,n-1 Ꮖ 1, . xi+10x+1 ≤ 10 i = 1,..., n − 1 ,...,xn≥0 a) (No written answer to this question is required.) Let n = 4. Introduce slack variables w1,..., wg and an artificial variable xo representing con- straint tolerance. Apply the online pivot tool https://vanderbei.princeton.edu/JAVA/pivot/simple.html in order to find a feasible solution to CUBE by means of Phase 1 of the Sim- plex algorithm. Verify that the dictionary after Phase 1 (the column corresponding to x deleted and restored in row 0) is: 10000 + 10000 + 1000 W3 + 110 5 + 17 1 S = 1 x1 = - 10 աշ = x2 = - 100 W4 = 95 49 - 1 x3 - = 1000 W6 = 499 50 - 1 = W8 =わ 10000 4999 500 -ひく -ひく 100 15 -ひく1 1000 -ひく1 W1 W1 w1 W1 10000 W1 1 500 W1 - W3 - - - - - 15 1 1000 W3 W3 w3 W3 W3 - - - - ws W5 TW5 100 W5 15 w5 - - W7 W7

I need help with the attached question please parts a,b,and c

Construct a PYTHON program code for an inequality constraint minimization via logarithm barrier method.(OPTIMIZATION) For this problem minimize –x + /y subject to (x – 5)2 + (y – 3)2 < 3/2 x < 5 -

Let A be a n x m matrix of 0's and 1's. Design a dynamic programming O(nm) time algorithm for finding the largest square block of A that contains 1's only. When designing the dynamic programming algorithm, please describe the size and dimensionality of the dynamic programming table, and explicitly formulate the recurrence relationship. Hint: Define the dynamic programming table 1(i, j) be the length of the side of the largest square block of 1's whose bottom right corner is A[i, j].

The branching part of the branch and bound algorithm that Solver uses to solve integer optimization models means that the algorithm [a] creates subsets of solutions through which to search[b] searches through only a limited set of feasible integer solutions [c] identifies an incumbent solution which is optimal [d] uses a decision tree to find the optimal solution 2. The LP relaxation of an integer programming (IP) problem is typically easy to solve and provides a bound for the IP model. [a] True [b] False

Develop a simulated annealing procedure in either R or Python to solve the following knapsack problem: (Note, this problem can be solved to optimality using integer programming; however, the focus of this question is on developing the simulated annealing method). Maximize: 12x1 + 16x2 + 22x3 + 8x4 S.T. 4x1 + 5x2 + 7x3 + 3x4 ≤ 14 xi ~ binary for all i

2. The simplex tableau below is an intermediate step resulted from solving a linear programming problem using simplex method. (1) What is the current basic feasible solution? Is the current solution optimal, why? (2) If the current solution is not optimal, identify the pivot element and complete Gaussian Elimination for the pivot row and the first row of the tableau in the next iteration. Then, answer the following questions: which variables are the basic variables at iteration 2? Is the solution from Iteration 2 likely to be optimal, and why? Iteration 1: Π x1 x2 x3 s1 s2 s3 s4 s5 constant 1 0 -200 -100 0 0 300 0 0 15000 0 0 10 2 1 0 -16 0 0 200 0 0 4 2 0 1 -8 0 0 100 0 1 0 0 0 0 1 0 0 50 0 0 1 0 0 0 0 1 0 80 0 0 0 1 0 0 0 0 1 150 Iteration 2: Π x1 x2 x3 s1 s2 s3 s4 5ドル constant

Answer 5,6,7,8

Need help understanding Linear Programming in my optimization class.

Consider the set 6x +12y + 4z = 70, 7x - 2y + 3z = 5, and 2x + 8y9z = 6. Determine the best option for performing left division on these linear algebraic equations. Multiple Choice A = [6, 12, 4; 7, -2, 3; 2, 8, -9]; B = [70; 5; 64]; Solution = A/B A = [6, 12, 4; 7, -2, 3; 2, 8, -9]; B = [70; 5; 64]; Solution A\B A = [6, 12, 4; 7, -2, 3; 2, 8, -9]; B = [70, 5, 64]; Solution A/B A = [6, 12, 4; 7, -2, 3; 2, 8, -9]; B = [70, 5, 64]; Solution A\B

esc A Question 14 of 20: Select the best answer for the question. 14. Use Gauss-Jordan elimination to solve the following linear system: -3x + 4y = -6 5x - y = 10 O A. (2,0) O B. (2,-5) OC. (-6,2) O D. (2,2) O Mark for review (Will be highlighted on the review page)> ← 21 W = S #3 E D لم G $ 4 { R بر 19 F % 50 F ف Oll GY O U *00 C 8 A

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Please answer question.