Problem 5(4 points): Solve following LP problem by Simplex Algorithm Mar = 11 +12 subject to 2r1t...
5. Solve the following LP problem using Phase I and Phase II simplex algorithm. Maximize f(X) = x1 + x2, subject to: 4x1-2x2 8 XI6 X1, X20 5. Solve the following LP problem using Phase I and Phase II simplex algorithm. Maximize f(X) = x1 + x2, subject to: 4x1-2x2 8 XI6 X1, X20
*5. Solve the following LP problem using two-phase Simplex method: Maximize f- 4x1x2 X3 subject to 2х1 + X2 + 2хз - 4, Зх1 + 3x2 + хз 3 3, х120, х2 2 0, хз 2 0. Note: Since a BFS is not available, start Phase I simplex algorithm by introducing two artificial variables] *5. Solve the following LP problem using two-phase Simplex method: Maximize f- 4x1x2 X3 subject to 2х1 + X2 + 2хз - 4, Зх1 + 3x2...
*5. Solve the following LP problem using two-phase Simplex method: Maximize f= 4x1+ x2 + x3 subject to: 2x1x22x3= 4 Зх1 +3x2 + хз %3D 3, X12 0, х2 20, х3 2 0. [Note: Since a BFS is not available, start Phase I simplex algorithm by introducing variables] two artificial *5. Solve the following LP problem using two-phase Simplex method: Maximize f= 4x1+ x2 + x3 subject to: 2x1x22x3= 4 Зх1 +3x2 + хз %3D 3, X12 0, х2 20,...
Use the simplex algorithm to solve the following LP ??? ?=4?1 +4?2 ?.?. ?1−2?2 ≤3 2?1 + ?2 ≤ 5 5?1 + ?2 >= 7 ?1, ?2 ≥ 0
4) (20 pts) Consider the following optimal Simplex Tableau of an LP problem: 11 12 13 0 0 0 14 -4 1 RHS -2-40 0 1 1 1 It is known that 14 and 15 are the slack variables in the first and the second constraints of the original problem. The constraints are stype. Write the original problem.
SIMPLEX METHOD Solve the following problem using simplex method LP MODEL Let X1 no. of batches of Bluebottles X2 no. of batches of Cleansweeps Objective: Max Z-10X1+20X2 Subject to: 3X1 4X2 S 3 Plant 1 assembly capacity constraint -X1 2-5 5X1 +6X2 s 18 Z, X1, X2 20 Plant 2 capacity constraint Plant 3 capacity constraint
Problem 3. (a) Solve the following LP problem using the Simplex Method. Use the smallest- subscript rule to choose entering and leaving variables. Show all steps. maximize xi+ 5.02 + 5x3 + 524 subject to X1+ 412 + 3x3 + 3x4 < 17 12 + x3 + x4 <4 Xit 202 + 2x3 + 3x4 < 10 X1, ..., 84>0. (b) Is the optimal solution you found the only one? Explain.
Solve the following LP problem using the Simplex Method. Type out all work. (Use the table function 3. with borders to create your tableaux.) Maximize subject to x + 3y +zS15 3x 2y +zs 25 x20,y2 0, z20
3. Use the two-phase simplex method to solve the following LP. Min z = x1 + 2x2 Subject to 3x1 + 4x2 < 12 2x1 - x2 2 2 X1, X2 20
Problem 3 Consider the LP problem Minimize -3r22 0s1+0s2 +0s3 0s Subject to 228 2r2 + $2 1,2,81,82 8384 with optimal tableau as follows: sic r1 T2 s1 s2 s3 s4 Solution C 0 0 20 1 0 0 12 Optimum 0 30 0-103 4 0 021 2 Find the dual optimal solution and the corresponding objective function value using the information provided in the optimal simplex tableau. Problem 3 Consider the LP problem Minimize -3r22 0s1+0s2 +0s3 0s Subject...