Glenmont Corporation wants to select 1 project from a set of 4 possible projects. Which of these constraints ensures only 1 project is selected?     X1 + X2 + X3 + X4 ≥ 0      X1 + X2 + X3 + X4 ≥ 1     X1 + X2 + X3 + X4 = 1     X1 + X2 + X3 + X4 ≤ 1

Introduce slack variables as necessary and write the initial simplex tableau for the problem.Maximize z = 2x1 + x2  subject to: x1 + x2 ≤ 71  3x1 + x2 ≤ 175   x1 ≥ 0, x2 ≥ 0

Consider the problemMaximize z = x1 + 5x2 + 3x3subject tox1 + 2x2 + x3 = 62x1 - x2 = 8x1, x2, x3 >= 0The variable x3 plays the role of a slack. Thus, no artificial variable is needed in the firstconstraint. In the second constraint, an artificial variable, R, is needed. Solve the problemusing x3 and R as the starting variables.

Find X₁ and X₂ that maximize the objective function Z = 3x₁ + 5×₂2 with the constraint function 2x, 8 3X₁ ≤ 15 6X₁ + 5X₂ > 30 = Using the simplex method.