Question

In: Advanced Math

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.

Solutions

Expert Solution

IIn this using M-method


Related Solutions

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
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
For the following linear programming problem:    Maximize z = 2x1+ x2    Such that     ...
For the following linear programming problem:    Maximize z = 2x1+ x2    Such that      x1+ 2x2 ≤ 12          x2 ≥ 3       x1,x2 ≥ 0 (a) Write the first two constraints in equation form by adding slack or subtracting excess (surplus) variables. (b)Find all basic solutions for this LP (c) Which of these solutions are feasible? (d)Which of these feasible solutions is optimal? Find the optimal value of z
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT