4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...

4.Maximize: Z = 2X1+ X2-3X3

Subject to: 2X1+ X2= 14

X1+ X2+ X3≥6

X1, X2, X3≥0

Solve the problem by using the M-technique.

Expert Solution

IIn this using M-method

Colby Messinger answered 2 years ago

Maximize Z= 3 X1+4 X2+2.5X3 Subject to 3X1+4X2+2X3≤500 2X1+1X2+2X3≤400 1X1+3X2+3X3≤300 X1,X2,X3≥0 Change objective function coeffiecient x3...

Maximize Z= 3 X1+4 X2+2.5X3 Subject to 3X1+4X2+2X3≤500 2X1+1X2+2X3≤400 1X1+3X2+3X3≤300 X1,X2,X3≥0 Change objective function coeffiecient x3 to 6 and change coefficient of x3 to 5in constraint 1 ,to 2 in constraint 2 ,to 4 in constraint3. calculate new optimal solution using sensitivity analysis

Given the following primal problem: maximize z = 2x1 + 4x2 + 3x3 subject to x1...

Given the following primal problem: maximize z = 2x1 + 4x2 + 3x3 subject to x1 + 3x2 + 2x3 ≥ 20 x1 + 5x2 ≥ 10 x1 + 2x2 + x3 ≤ 18 x1 , x2 , x3 ≥ 0 1. Write this LP in standart form of LP. 2.Find the optimal solution to this problem by applying the Dual Simplex method for finding the initial basic feasible solution to the primal of this LP. Then, find the optimal...

By using Big-m method Minimize z=4x1+8x2+3X3subject to x1+x2>=2, 2x1+x3>=5 and x1,x2,x3>=0

Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove...

Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove that U is a subspace of F4. (b) Find a basis for U and prove that dimU = 2. (c) Complete the basis for U in (b) to a basis of F4. (d) Find an explicit isomorphism T : U →F2. (e) Let T as in part (d). Find a linear map S: F4 →F2 such that S(u) = T(u) for all u ∈...

Consider the problem maximize Z = 5 x1 + 3 x2 + 2 x3 + 4...

Consider the problem maximize Z = 5 x1 + 3 x2 + 2 x3 + 4 x4 subject to 5 x1 + x2 + x3 + 8 x4 = 10 2 x1 + 4 x2 + 3 x3 + 2 x4 = 10 X j > 0, j=1,2,3,4 (a) Make the necessary row reductions to have the tableau ready for iteration 0. On this tableau identify the corresponding initial (artificial) basic feasible solution. Also, identify the initial entering and...

Consider the following problem Maximize Z=2x1 + 5x2 + x3 subject to 4x1+...

Consider the following problem Maximize Z=2x1 + 5x2 + x3 subject to 4x1+ 2x2 + x3 ≤ 6 x1 + x2 ≤ 2 xi ≥ 0 for i=1,2,3 a. Inserting slack variables, construct the initial simplex tableau. What is the initial basic feasible solution? b. What is the next non-basic variable to enter the basis c. Using the minimum ratio rule, identify the basic variable to leave the basis. d. Using elementary row operations, find...

MAXIMIZATION BY THE SIMPLEX METHOD Maximize z = x1 + 2x2 + x3 subject to x1...

MAXIMIZATION BY THE SIMPLEX METHOD Maximize z = x1 + 2x2 + x3 subject to x1 + x2 ≤ 3 x2 + x3 ≤ 4 x1 + x3 ≤ 5 x1, x2, x3 ≥0

Find dual from primal conversion MIN Z = x1 - 2x2 subject to 4x1 - x2 >= 8 2x1 + x2 >= 10 -x1 + x2 <= 7 and x1,x2 >= 0

Find dual from primal conversion MIN Z = x1 - 2x2 subject to 4x1 - x2 >= 8 2x1 + x2 >= 10 -x1 + x2 = 0

Exercise Solve the following linear programs graphically. Maximize Z = X1 + 2X2 Subject to 2X1...

Exercise Solve the following linear programs graphically. Maximize Z = X1 + 2X2 Subject to 2X1 + X2 ≥ 12 X1 + X2 ≥ 5 -X1 + 3X2 ≤ 3 6X1 – X2 ≥ 12 X1, X2 ≥ 0

If there are 3 known functions, namely: X1 + 2X2 + 3X3 = 6 2X1 -...

If there are 3 known functions, namely: X1 + 2X2 + 3X3 = 6 2X1 - 2X2 + 5X3 = 5 4X1 - X2 - 3X3 = 0 Use the Jacobian determinant to see whether there is a functional freedom function for each pair. Determine the values of X1, X2 and X3 in the above equation?

Question