Find the set of ALL optimal solutions to the following LP: min z= 3x1−2x2 subject to...

Find the set of ALL optimal solutions to the following LP: min z= 3x1−2x2 subject to 3x1+x2≤12 3x1−2x2−x3= 12 x1≥2 x1, x2, x3≥0

Expert Solution

Colby Messinger answered 2 years ago

Consider the following LP model.Max Z = 3x1 - 4x2 + x3 subject to x1 + x2 +...

Consider the following LP model.Max Z = 3x1 - 4x2 + x3 subject to x1 + x2 + x3 >= 9 2x1 + x2 + x3<= 12 x1 + x2 = 5 x1, x2, x3 >= 0 Change it to standard form. Obtain all the basic solutions and indicate which ones are basic feasible solutions and write down the corresponding corner points. For each basic solution, you have to obtain the values of all the variables. Obtain the solution of the LP...

For the following LP problem, determine the optimal solution by the graphical solution method. Min Z=...

For the following LP problem, determine the optimal solution by the graphical solution method. Min Z= 3x1+2x2 Subject to 2x1+x2 >10 -3x1+2x2 < 6 X1+x2 > 6 X1,x1 > 0 Graph and shade the feasible region

(Operation Research II Industrial Engineering) Consider the following LP: Minimize z = x1 + 2x2 Subject...

(Operation Research II Industrial Engineering) Consider the following LP: Minimize z = x1 + 2x2 Subject to x1 + x2 >= 1 -x1 + 2x2 <= 3 x2 <= 5 x1,x2 >= 0 (a) Convert the LP given above to the standard form. Determine all the basic feasible solutions (bfs) of the problem. Give the values of both basic and nonbasic variables in each bfs. (b) Identify the adjacent basic feasible solutions of each extreme point of the feasible region....

maximize z = 2x1+3x2 subject to x1+3X2 6 3x1+2x2 6 &nb

maximize z = 2x1+3x2 subject to x1+3X2 6 3x1+2x2 6 x1,x2 This can be simply done by drawing all the lines in the x-y plane and looking at the corner points. Our points of interest are the corner points and we will check where we get the maximum value for our objective function by putting all the four corner points. (2,0), (0,2), (0,0), (6/7, 12/7) We get maximum at = (6/7, 12/7) and the maximum value is =...

Find the optimum solution to the following LP by using the Simplex Algorithm. Min z =...

Find the optimum solution to the following LP by using the Simplex Algorithm. Min z = 3x1 – 2x2+ 3x3 s.t. -x1 + 3x2 ≤ 3 x1 + 2x2 ≤ 6 x1, x2, x3≥ 0 a) Convert the LP into a maximization problem in standard form. b) Construct the initial tableau and find a bfs. c) Apply the Simplex Algorithm.

Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 –...

Consider the following linear program. Maximize z= 5x1+ 3x2 subject to 3x1+ 5x2≤15 5x1+ 2x2≤10 – x1+ x2≤2 x2≤2.5 x1≥0, x2≥0 a. Show the equality form of the model. b. Sketch the graph of the feasible region and identify the extreme point solutions. From this representation find the optimal solution. c. Analytically determine all solutions that derive from the intersection of two constraints or nonnegativity restrictions. Identify whether or not these solutions are feasible, and indicate the corresponding objective function...

Find the dual of the following LP, using direct method. minz=4X1 +2X2 -X3 subject to X1...

Find the dual of the following LP, using direct method. minz=4X1 +2X2 -X3 subject to X1 +2X2 ≤6 X1 -X2 +2X3 =8 X1 ≥0,X2 ≥0,X3 urs

Solve the following set of equations with LU factorization with pivoting: 3x1 -2x2 + x3 =...

Solve the following set of equations with LU factorization with pivoting: 3x1 -2x2 + x3 = -10 2x1 + 6x2- 4x3 = 44 -8x1 -2x2 + 5x3 = -26 Please show all steps

Given the following LP max z = 2x1 + x2 + x3 s. t. 3x1 -...

Given the following LP max z = 2x1 + x2 + x3 s. t. 3x1 - x2 <= 8 x2 +x3 <= 4 x1,x3 >= 0, x2 urs (unrestricted in sign) A. Reformulate this LP such that 1)All decision variables are non-negative. 2) All functional constraints are equality constraints B. Set up the initial simplex tableau. C. Determine which variable should enter the basis and which variable should leave.

Find all basic feasible solutions for the following LP and identify the adjacent basic feasible solutions...

Find all basic feasible solutions for the following LP and identify the adjacent basic feasible solutions of each basic feasible solution. max z= 3x1 +5x2 s.t. x1 <4 2x2 < 12 3x1 +2x2 < 18 x1>0, x2>0

Question