Question

Consider the following linear programming problem: Maximize z = 4x1 + x2 Subject to: 3x1 + x2 ? 6 5x1 + 3x2 ? 15 x1, x2 ? 0 a) Find a range of values on the coefficient of x1 in the objective function for which the current basis remains optimal. b) Find a range of values on the coefficient of x2 in the objective function for which the current basis remains optimal. c) Find the range of values for the RHS of the first constraint for which the current basis remains optimal. Determine the new optimal solution if the RHS is 6+?. d) Find the range of values for the RHS of the second constraint for which the current basis remains optimal. Determine the new optimal solution if the RHS is 15+?. e) If the RHS of the first constraint is 8, what is the new optimal objective function value?

          Consider the following linear programming problem:

Maximize z = 4x1 + x2

Subject to:
3x1 + x2 ? 6
5x1 + 3x2 ? 15
x1, x2 ? 0

a) Find a range of values on the coefficient of x1 in the objective function for which the current basis remains optimal.
b) Find a range of values on the coefficient of x2 in the objective function for which the current basis remains optimal.
c) Find the range of values for the RHS of the first constraint for which the current basis remains optimal. Determine the new optimal solution if the RHS is 6+?.
d) Find the range of values for the RHS of the second constraint for which the current basis remains optimal. Determine the new optimal solution if the RHS is 15+?.
e) If the RHS of the first constraint is 8, what is the new optimal objective function value?

Consider the following linear programming problem:

Maximize z = 4x1 + x2

Subject to:
3x1 + x2 ? 6
5x1 + 3x2 ? 15
x1, x2 ? 0

a) Find a range of values on the coefficient of x1 in the objective function for which the current basis remains optimal.
b) Find a range of values on the coefficient of x2 in the objective function for which the current basis remains optimal.
c) Find the range of values for the RHS of the first constraint for which the current basis remains optimal. Determine the new optimal solution if the RHS is 6+?.
d) Find the range of values for the RHS of the second constraint for which the current basis remains optimal. Determine the new optimal solution if the RHS is 15+?.
e) If the RHS of the first constraint is 8, what is the new optimal objective function value?

Added by Antonio M.

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