Exam 2: An Introduction to Linear Programming

All of the following statements about a redundant constraint are correct EXCEPT

Does the following linear programming problem exhibit infeasibility, unboundedness, or alternate optimal solutions? Explain. Min 1X + 1Y s.t. 5X + 3Y $\ge$ 30 3X + 4Y $\ge$ 36 Y $\ge$ 7 X , Y $\ge$ 0

The constraint 5x₁ -2x₂ $\le$ 0 passes through the point (20, 50).

Find the complete optimal solution to this linear programming problem. Min 5X + 6Y s.t. 3X + Y $\ge$ 15 X + 2Y $\ge$ 12 3X + 2Y $\ge$ 24 X , Y $\ge$ 0

For the following linear programming problem, determine the optimal solution by the graphical solution method Max -X + 2Y s.t. 6X - 2Y $\le$ 3 -2X + 3Y $\le$ 6 X + Y $\le$ 3 X , Y $\ge$ 0

A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called

Explain the difference between profit and contribution in an objective function. Why is it important for the decision maker to know which of these the objective function coefficients represent?

And the complete optimal solution to this linear programming problem. Max 5X + 3Y s.t. 2X + 3Y $\le$ 30 2X + 5Y $\le$ 40 6X - 5Y $\le$ 0 X , Y $\ge$ 0

The standard form of a linear programming problem will have the same solution as the original problem.

A constraint that does not affect the feasible region is a

Solve the following system of simultaneous equations. 6X + 4Y = 40 2X + 3Y = 20

Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in the optimal values of the decision variables, but a change in the right-hand sides of a binding constraint does lead to new values.