2 Find the optimal solution to the following madhah problem max z Ax +B x2 A=6 s.t. 2x, + 4x2 s 12, -X1 + 2x2 S 2, X1, X2 2 0. B=1

Q: 1. a. Show that this model has an unbounded solution by Big M Method. b. What can be changed to have…

A: According to the given information, it is required to first show that the given equation has…

Q: 4. Solve the following model graphically Lexicographically minimize a = {(p1 + p2), (n3). (p4), (n1…

A: The complete solutions are given below

Q: O 3. Solve the following problem (assuming it has a solution) minimize 4 In(x + 2) + y subject to…

A: According to you we need to solve only question no. (3). (3) minimize 4lnx2+2+y2Subjected…

Q: 8.1.4 If cx = x1 +x2 + 3x3 is minimized subject to x1 + x2 + X3= 1, x> 0, show that two corners of…

A: Consider the given information.

Q: max   –x1 – 2x2 s.t.   x1 –  x2 ≤ 6        x1 + 2x2 ≥ 4        x1, x2 ≥ 0 For the LP problem…

A: The given LPP is as follows  max -x1-2x2 subject to  x1-x2≤6x1+2x2≥4x1,x2≥0 to solve the LPP using…

Q: 1. we are making 3 products (X1, X2, and X3). The products require assembly, machine process 1,…

A: According to the given information, it is required to solve the LP problem.

Q: Solve the following LP problems using Simplex Method. Minimize P = y1 – 3y2 + 2y3 Subject to : Зу1 —…

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Q: Determine the dual of the minimization problem. min z = 9x, + 4x + 10x3 s.t. 2x1+ x2 + 3x3 26 6x1+…

A: Given minimization problem is: min z=9x1+4x2+10x3 subject to 2x1+x2+3x3≥66x1+x2+x3≥9x1, x2, x3≥0 We…

Q: 5. Solve the following maximization problem U (x, y) = x³ +24y max {x,y} s.t. x + 2y = 10 where x 20…

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Q: 2) Find all the critical points of each of the following systems: c) x' = xy – x² У' 3 х? — 2ху — у?

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Q: Consider the LPP: Max. z = 120 x1 +100 x2 %3D S. t. 2 x1 + 2 x2 s 8 5 x1 + 3 x2s 15 X1, X2 2 0 One…

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Q: Q#3: (i) Solve problem by first finding the dual and then using the simplex algorithm. Minimize (E c…

A: The dual will be:  maximize: 32x1+112x2+54x3 Subject to:  8x1+7x2+x3≤225x1+4x2+6x3≤180

Q: b) Consider the following LP problem. Maximize z = 3x1 + 4x2 + X3 Subject to X1 + x2 + x, 5 50 2x, –…

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Q: . Solve by optimal control the problem: max 68. s.t. [ (ux − u² − x² )dt 1 x'=x+u, x(1)=2, x(5) =…

A: As per the question we are given a optimization problem where we have to find the optimal control…

Q: 7. Minimize C=5x+2y x+3 y215 Subject to 2 x+ y2 20 x, y20

A: Find the attachment

Q: Q2) Consider the following LP problem and its optimal solution. Max z = 4x1 + 7x2 x1 х2 St Зx1 + 6х2…

A: If we have primal for the from ' Max Z = CTX Subjected to: AX≤B (constraints)and X≥0 Let 'n' be no.…

Q: 1. a. Show that this model has an unbounded solution by Big M Method.     b. What can be changed to…

A: 1. (a) Given,               Max Z=3x1+6x2subject to       3x1+4x2≥12    -2x1+x2≤4and      x1, x2≥0

Q: Problem 3 Solve the following LP of normal maximization form by the simplex method and obtain the…

A: The simplex method (BigM method) Max z=y1+y2-2y3subject to y1+2y2≤5y1-y2-3y3≤4and y1≥0,y2≥0,y3≥0 The…

Q: The solution to the problem. =b, max f(x, X2. Xg)=x, + Xg subject to for b, =1 and by =2 is (k,X)=2,…

A: Given- The solution to the problem  max fx1, x2, x3 = x1 + x3subject tox12 + x22 = b1x1 + x2 + ex3 =…

Q: Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 +…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Q4: Consider the following LP Max z= 3x1 -3x2 Subject to: -X1 + 4x2 2 8 X1 + X2 5 6 X12 0, x2…

A: (A) The Given Linear Programming problem is- Max Z =3x1-3x2subject to:-x1 + 4x2 ≥ 8x1 + x2 ≤ 6x1 ≥ 0…

Q: 1. Consider problem min xí + x5 s.t. ai + x3 0. Verify that the KKT necessary and sufficient…

A: We are given a non-linear optimization problem. min x12+x22subject…

Q: Consider the following L.P. Problem: Max.Xo= 3 x1 +12 x2 Subject to: 2x1 + X2 ≤12 3x1 + 4X2 ≥ 21…

A: The given LPP is            Max   X0=3x1+12x2 subject to:           2x1+x2≤123x1+4x2≥21x1≥3x1≥0,…

Q: Max Z=5X1+2X2 S.T. 2X1+5X2 <10 4X1 - X2 s 12 X1+X2 < 4 X1,X2 2 0 Optimal solution is X1=3, X23D0 Z=…

A: We will solve yhis problem by using graphical method. First draw the given regions in the graph.…

Q: 1. Consider the problem below: Min (z) = -2x-×2 Subject to: X1 + X25 5 2x1 + 3x2 S 12 X1 5 4 X1, X2…

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Q: Find the optimal solution of the following problem. Min Ex+ 11Y s.t ex+ 3Y 2 27 7x+ 6Y 2 42 4x+ BY 2…

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Q: Use the Big-M method to find an initial basic feasible solution for the following LP: max z = 3x +…

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Q: Q2): Dual problem below: Min Z = 120yı + 6y2 + 105y3 Subject to : 3y1 + 5y2 + 8y3 2 3 10y, + 2y2 +…

A: Given Dual problem belowMin z=120y1+6y2+105y3Subject…

Q: e the following constrained optimization problem using the method of Lagrange multipliers: max (x³ +…

A:

Q: H.W/ using dual simplex method to solve the following L.P problems: 1) Min Z = 3x1 +2x2+3x3…

A: The given problem is Min Z=3x1+2x2+3x3 sub to x1+4x2+x3≥72x1+x2+x4≥10x1, x2, x3, x4≥0

Q: 7. Obtain the dual of the LP problem : z= xỊ + x2 + X3. Subject to the constraints: XI – 3x2 + 4x3 =…

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Q: 2. Consider the following optimization problem: max x, (30 – x, ) +x, (50 – 2x, ) – 3.x, – 5x, –…

A: The objective is to state the KKT conditions and solve the optimization problem max…

Q: Solve the following LP problems using the simplex method Question 1 max Z= 3x,+ 2x,+ x3 s/t 2x,+…

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Q: Маx Z=5X1+2X2 S.T. 2X1+5X2 <10 4X1 - X2 < 12 X1+X2 < 4 X1,X2 2 0 Optimal solution is X1=3, X2=0 Z=…

A: We will solve the given LPP problem using the graphical method first we will find the region which…

Q: (d) The Cauchy problem u, + 2 uy = 0, u(x, y) = x² on y = r has: (A) a unique solution (C)…

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Q: -pply Big-M method to solve the following L. P. P. : Maximize : z = x1 + 2x2 + 3x3 – X4 ubject to :…

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Q: Question 2 Consider the following LP: Minimize Z = 3x, +5x, Subject to 3x, -2x, 2 12 - 2x, + x, <6…

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Q: 6.12 Consider the problem minimize f(æ) subject to x € N, where f: R? {x = [x1, c2]T : xỉ + *2 2 1}.…

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Q: 2.6 Convert the original LP problem into LP standard form. maximize ) = -x, + 2x2 - x3 + 3x4 s.t. X1…

A: The given problem is to convert the given original linear programming problem to the standard form…

Q: The following table shows an optimal solution for an LPP. Basic Variables 6. X2 4. X1 X3 slack 1…

A: DEGENERACY. Degeneracy in a linear programming problem is said to occur when a basic feasible…

Q: (b) Consider the problem Maximize Z= +2x, 3x +4x3 Subject to 2r +3.x +5x) 2 2 3x + +x: 7x 5 3 + 4x…

A: Given LPP is Maximize Z=2x1+3x2+4x3Subject to2x1+3x2+5x3≥23x1+x2+7x3≤3x1+4x2+6x3≤5x1,x2≥0, x3…

Q: 4. As an engineer and a scientist, a research has been conducted and the problem has been modeled…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Consider the following LP. Max z = 4x, +8x, +8x, – 6x, subject to X, + X, + X3 = 4 X, + 4x, +x4 = 8…

A: We are given the following LPP : Max Z = 4x1 + 8x2 + 8x3 - 6x4 Subject to the constraints : x1 + x2…

Q: Consider the following LPproblem 2x1+3r2 marimize z = %3D 3x2 0 (non negativity const a. The…

A: Let us solve this problem graphically Let us consider the 1st constraint as -x1+3x2=12 x1 0 -12…

Q: 1. a. Show that this model has an unbounded solution by Big M Method. b. What can be changed to have…

A: Given Max Z = 3x1 + 6x2      Subject to 3x1 + 4x2 ≥ 12…

Q: Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 +…

A: (a) First find primal to dual of LPP :  Primal is (Solution steps of Primal by BigM method)  MIN Zx…

Q: EXAMPLE: (0,0) 3x-2y 26 5x+45 O > 5 x a 1915 CRITICAL POINTS -A (30) ( B (2.0) 1 D ( ¾/5,9). ✓c…

A: