We are to minimize P = 3a+2b subject to the following constraints. a+b 24 3a+b 26 a, b 20 What is the dual problem in matrix form? 1 1 4 3 16 3 20 1 1 4 O b. 3 16 1 1 0 [1 33 1 1 2 C. 4 6 0 a.

Q: Consider the following system of linear equations 4 4 -2 30 1 0 18-0 7 -2 -3 2 -18 Which one, among…

A:

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: 3. Minimize: Z = 20x + 10y and the constraints are : x + 2y < 40, 3x + y 2 30, 4x + 3y 2 60, x 2 0,…

A:

Q: The number of constraints in each of the following hypotheses is (1) B1 + B2 = B3 = B4 (ii) Bz and…

A: The constraints are nothing but the total number of equations involved in the given hypothesis.…

Q: Question 12 In the given constraints, which solution is a feasible solution for a minimization…

A:

Q: 3. Given any basic feasible solution to a LPP (where the objective is to minimize the objective…

A: We will use basic knowledge of linear programming and optimization theory to answer this question.

Q: n the following problem, a minimization problem, the corresponding dual problem, and the final…

A: Solution a: Given maximization is maximize P  12y1+17y2 subject to 2y1+3y2≤155y1+7y2≤36y1, y2≥0 Now…

Q: Consider the following system of linear equations 4 -2 4 -2 1 X2 -12 -5 -3 2 X3 -37 Which one, among…

A:

Q: Consider the linear programming problem min c"x s.t. Ax = b x2 0 where A is a m x n matrix with m =…

A: We will use proof by contradiction to show that the given statement is true. For that we will first…

Q: Solve the system Ax=b using Gauss Jordan Elimination 2 1 1] [0] | A= b=9 1 3 2. 4 -2 5

A:

Q: following is the converted constraint of 3x + 2y  ≥ 35 under minimization of profit in simplex…

A: Since, constraint is of type &gt;= , we should subtract surplus variable S and add artificial…

Q: Given the following set of linear equations: X1 +x2 +5x3 = -21.5 -3x, + 6x2 +2x3 =-61.5 %3D 10x1…

A: Given: A system of equations, x1+x2+5x3=-21.5-3x1+6x2+2x3=-61.510x1+2x2-x3=27

Q: Consider the following simplex tableau: 3 10 0 12] 4 5 0 1 0 40 -6 -7 0 0 1 0 Which column (1, 2, 3…

A: We are given the Simplex tableau to be the following.                                2  3100  4…

Q: 2. Find the dual of the LP problem given below Z max = 4x1 + 2x2 + 5x3 Constraints: X1+ x2 2 2 3x1 +…

A: Given Primal LPP is, Z max =4x1+2x2+5x3 Subject to, x1+x2≥23x1+x2-x3≤125x1+2x2+3x3≤15x1,x2,x3≥0

Q: Consider the minimization problem: Minimize P(w1,w2,w3)=5w1+6w2+4w3, Subject to w1+2w2≥6…

A: consider the minimization problem Pw1, w2, w3=5w1+6w2+4w3 subject to  w1+2w2≥65w1+3w2+3w3≥24w1 , w2,…

Q: Consider the following system of linear equations -1 4 -2 13 -3 0 1 18-0 = -0 -3 2 Which one, among…

A:

Q: A simplex matrix for a standard maximization problem is given. 8 10 0 3 0 8 0 1 0 -1 0 -7 -11 0 0 1…

A: Find value x1 , x2 , x3 and s1 , s2 ,s3

Q: If the constraint of LP problem is 4A+3B ≤ 12, let B=3 then A will be a. 4 O b. 3.5 O c. 1.3 O d.…

A:

Q: 2. Use Gauss-Jordan row reduction to solve the system. 3x y - 2z -4 + = 2x Зу + 2z = 11 + y + z За.…

A:

Q: Write a simplex matrix for the following standard maximization problem: Maximize f = lx – 2y subject…

A:

Q: 3. Let a be the number of pills of Palium taken daily and b be the number of pills of Timade taken…

A:

Q: Consider the following simplex tableau: 2 3 1 0 0 12 4 5 0 1 0 40 -7 0 0 1 Which column (1, 2, 3 ,4,…

A: We have to find which column (1, 2, 3,4, 5 or 6) is the pivot column,   what is the test ratio…

Q: Maximize z= 5R+8P Subject to R+3/2P≤900 1/2R+1/3P≤300 1/8R+1/4P≤100 R,P  ≥ 0 1.Which of the…

A:

Q: 2. Determine (a) (b) (c) 1 0 0 if a solution to the linear system exists. If so, is it unique? 3 0 0…

A:

Q: A. Solve the following linear program by the solver method. C = 22x + 18y 15x + 10y 2 230 10x + 6y 2…

A: Please check further steps for the solution.!

Q: Solve the following LPP graphically using ISO- profit method. maximize Z =100 + 100y Subject to the…

A: to solve the LPP first plot the inequalities on the graph and mark the feasible region. The first…

Q: Given the following LP, which of the following dual constraints corresponds to X1? - 3x2 Maximize…

A:

Q: Maximize P-9z1 + 11z subject to the constraints 22 S 11 22 < 39 321 + 921 2120 How many slac…

A:

Q: A simplex matrix is given for which the associated maximization problem either has no solution or…

A: Here, swapping row 3 with row 1, 1 -1 0 0 0 5 0 3 0 5 -3 0 1 -7 0 7 0 20 -3 1 0 -4 0 5 0 -9…

Q: A simplex matrix for a standard maximization problem is given. 8 17 1 0 00 128 6 51 0 1 00 420 18 17…

A:

Q: Given the following set of linear equations: X₁ +x2 +5x3 = -21.5 -3x₁ + 6x2 +2x3 = -61.5 10x1 +2x2…

A: Given that x1+x2+5x3=-21.5-3x1+6x2+2x3=-61.510x1+2x2-x3=27

Q: Find r and h that minimize S subject to the constraint V = 54n.

A: Here V=54π and we should minimize  S=2πrh+2πr2 under the constraint V=54π=πr2h V(r,h)=πr2h-54π

Q: Express the following optimization problem as a standard linear program in matrix notation max zER?,…

A: Since I have solved similar ones ,let us write the given problem in matrix form

Q: - Consider the problem Маximize z %3D х, + 5х, + Зx; subject to X1 + 2x2 + xz = 6 2x1 - x2 = 8 X1,…

A: In standard form a linear programming problem is a minimization problem involving only equalities.…

Q: Assume that the following matrix is obtained at one of the steps when we use the simplex method to…

A: Since the most bottom row contains negetive value corresponding to the first column so it is not…

Q: Consider the quadratic programming problem minimize a"Qx + c"x subject to Ax = b x >0 where Q is a…

A: Note:- As per our guidelines, we can answer the first part of this problem as all the sub-parts are…

Q: O Consider the following linear program: minimise x1 + 2x2 - 6x3 subject to 4₁ - 8x2 + x3 = 10,…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the value of k for which the given linear system is stable: (use Gauss Elimination Method). 1 2…

A: To find the value of k using the gauss Jordan elimination method and reduce the given matrix into…

Q: 3. Find the dual of the LP problem given below. Z max = 4x, + 2x2 + 5x3 Constraints: X1 + x, 2 2 3x,…

A:

Q: Set up the simplex matrix used to solve the linear programming problem. Assume all variables are…

A: Given,Max f = 5 x + 3 y subject to 8 x + 5 y ≤ 300 x + 4 y ≤ 225 and x,y≥0 After introducing slack…

Q: Set up the method of Lagrange multipliers to minimize f(x,y,z)=6xy+xz subject to the constraint 2x +…

A:

Q: Solve applying the simplex method to the dual problem Minimize C= 6y, +8y, +12y, Subject to y +3y,…

A: Step:-1 Given primal problem is Minimize   C=6y1 +8y2 +12y3subject…

Q: | Consider the linear system Ax = b, where A = |1 1 and b = (0,2, 7). 1 2 | Find x, the least…

A: (a)Given  A=101112, b=027The least square solution x^ minimizes f(x^) = Ax-b2=101112x1x2-0272f(x^)=…

Q: 2. Find the general solution of the following linear system: X + 3z = 1 Зх + у = 1 None O (-3t + 1,…

A: We have: x+3z=13x+y=1 Now, we can write it in the form AX=b as : 103310xyz=11 Here, A=103310, X=xyz,…

Q: The number of constraints in each of the following hypotheses is (1) B1 + B2 = B3 = Ba B1 B2 (ii) =…

A: Given Information: Consider the given hypotheses:     i β1+β2=β3=β4ii β1β2=β3 and β4=1iii β1=1 and…

Q: Given the following unconstrained nonlinear programming problem, f(x1,X2, X3) = 2x+x,² +x;²= x,X2 -…

A:

Q: Maximize ƒ(x, y, z) = x2 + y2 + z2 subject to the constraints 2y + 4z - 5 = 0 and 4x2 + 4y2 - z2 =…

A:

Q: min     x1 +  x2 s.t.   3x1 + 2x2 ≥ 36        3x1 + 4x2 ≥ 48         x1, x2 ≥ 0 For the LP…

A: Given LP problem is Min z=x1+x2 Subject to 3x1+2x2≥363x1+4x2≥48 And x2,x2≥0 Solving the given LPP by…

Q: Complete the following. Minimize g = 8y1 + 7y2 subject to 3y1 + 4y, 2 24 Y1 + 4y2 2 16. (a) Form the…

A: