What is the constraint for node 3 in the following maximal flow problem?a.X13 + X23 - X34 ≤ 0b.X13 + X23 - X34 = 0c.X13 ≤ 5d.X13 + X23 + X34 = 0

The source node is the input node in a maximal flow problem.Group of answer choicesTrueFalse

Convert the following problem into an MIP. (Do not optimize) Max. Z = x_{1} + 2x_{2} + 5x_{3} s. t. | - x_{1} + 10x_{2} -3x 3 |>=15 2x_{1} + x_{2} + x_{3} <= 1 x_{1}, x_{2}, x_{3} >= 0

Maximize Z- 3x1 + 2x2 subject to constraints 2 x1 + x2 18 2x1+3x2=42 3 x1 + x2 ≥ 20 i. Prepare initial simplex table for the above LPP. ii. Also find entering vector and departing vector from this table.

For a minimum-cost flow problem to have a feasible solution, which of the following mustbe true?A) There is the same number of supply nodes and demand nodes.B) There is only one supply node and one demand node.C) There is an equal amount of supply and demand.D) The supply and demand must be integers.E) The transshipment nodes must be able to absorb flow.

Write the dual of the following linear programming problem:Maximize 8x1 + 3x2 − 2x3subject to x1 − 6x2 + x3 > 25x1 + 7x2 − 2x3 = −4x1 ≤ 0, x2 ≥ 0, x3 unrestricted.