Consider the simplex tableau given below. X1 X2 S1 S2 S3 5 1 4 1 3 1 10 2 1 4 - 6 - 2 5 (A) The pivot element is located in column
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- Consider the following LP:Maximize z = 16x1 + 15x2subject to40x1 + 31x2 <=124-x1 + x2<= 1x1<=3x1, x2 >= 0(a) Solve the problem by the simplex method, where the entering variable is thenonbasic variable with the most negative z-row coefficient.Consider the simplex tableau given below. a. Show the values after one pivot operation in the tableauQ3- Find the optimum values of X1, X2 and X3 that maximize the values of Z using simplex method? Maximize Z= 3X1+ 4X2+X3 Subject to 3X1 +10X2 +5X3 <120 5X1 +2X2 +8X3<6 4X1 +10X2 +3X3 < 105 X1,X2,X3 >0
- Determine the solutions of the LP model below using simplex method. Complete Tableaus 1 and 2 below by supplying the values for the items in red. Maximize: P=15x1 + 13x2 Subjec to: x1 ≤ 300 (place in R11) 2x1 + 3x2 ≤ 360 (place in R21) 3x1 + 5x2 ≤ 270 (place in R31) x1 ≥ 0, x2 ≥ 0Consider the following intermediate tableau (not the Initial Simplex tableau): p x1 x2 s1 s2 rhs 0 0 1 1/2 -1/2 3/2 0 1 0 1/2 1/2 5/2 1 0 0 2 -1 7 a) Determine the pivot column and the pivot element, and perform all the row operations for the entire pivot column to obtain the next new tableau. Once you have the new tableau, look at the numbers you have in the objective row and enter each one as requested in each box below. Note: Where applicable, fractions must be entered as 2/5, -1/3, and so on. Under column x1 in the objective row, you have: Under column x2 in the objective row, you have: Under column s1 in the objective row, you have: Under column s2 in the objective row, you have: Under column RHS in the objective row, you have: b) Given the new tableau that you obtained above, three interpretations are possible. In the box below, type or copy and paste whichever answer shown in boldface letters below that you think…3. Solve the LP problem using the dual simplex method. (Please follow the example structure below) minimize x1 + 45x2+ 3x3 subject to: x1 + 5x2 - x3 >= 4 x1 + x2 + 2x3 >= 2 -x1 + 3x2 + 3x3 >= 5 -3x1 + 8x2 - 5x3 >= 3 Х1, X2, X3 ≥ 0.
- Consider the simplex tableau given below.Use method of Lagrange multipliers to find the optimal solution. y= 20A-101.5V phi= A(230-47.7/V) - 5556 =0Solve the following LP model by Simplex Method and find x1, x2 and x3. Max Z= 4x1 + 2x2 +2x3 subject to 3x1 + 6x2 - 3x3 ≤ 90 3x1+x2+x3 ≤ 180 x1- x2 + x3 ≤ 60 x1, x2, x3 ≥ 0