7. Consider the feasible region shown below. Assume the origin (A) is feasible and the constraints are all constraints and the variables are all nonnegative. Suppose you wish to maximize ay+a+2a over this feasible region and you are currently at point G. Which variable should enter the basis in the first iteration of the simplex algorithm if we wish to maximize the objective function improvement after the first iteration?

Use the simplex method to solve the linear programming problem. Maximize subject to: A. The maximum is when x₁ = ₁ X₂ = ₁ S₁ = (Type integers or simplified fractions.) B. There is no maximum. with z = 10x₁ + 12x2 , S₂ = 4x₁ + 2x₂ ≤24 6x₁ + x₂ ≤50 2x₁ + 2x₂ ≤26 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. X₁ ≥ 0, X₂ ≥ 0 and s3 =

I tried putting the question in geoGebra but I can’t see the full/complete calculator input of that you put in GEOGEBRA. Please make sure the whole calculation is shown of what you put to get the graph because at the moment I can only see half of it. Also what are ALL the corner points for it so I can find optimal value and also the feasible region

Solve the following linear programs (LPs) using the simplex algorithm. • For each tableau you obtain, write the associated BFS and its objective value. • For each LP, find the complete optimal solution set and write it using appropriate mathematical notation. Use only the information in the tableaux to justify your answer. maximize z(x1, x2, x3) = subject to -2x1 + 4.x3 + 2.x3 0

Solve the linear programming problem in the attached image (excel solver or simplex tableau). Here x3 is unrestricted, so we have to take: x3=(x’3-x”3), also introduce slack and artificial variables.

Solve the linear programming problem by the simplex method. Minimize 5x + y subject to the constraints shown on the right. The minimum value of Mis (Type integers or fractions.) which is attained for x = and y = x + y2 3 4x ≥ 11 x20, y20

2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X1 x2 X3 S1 S2 S3 S4 55 S1 -2 0 1 10 0 0 3 3 0 -20 1 2 0 6 ུཚ་ 1 1 -300 1 0 2 -30 2 0 0 -1 1 4 -20 11 00-40-8