Discussion Questions 1. List at least four applications of linear programming problems. 2. What is a "corner point"? Explain why solutions to linear programming problems focus on corner points. 3. Define the feasible region of a graphical LP problem. What is a feasible solution? 4. Each linear programming problem that has a feasible region has an infinite number of solutions. Explain. 5. Under what circumstances is the objective function more important than the constraints in a linear programming model? 6. Under what circumstances are the constraints more important than the objective function in a linear programming model? 7. Why is the diet problem, in practice, applicable for animals but not particularly for people? 8. How many feasible solutions are there in a linear program? Which ones do we need to examine to find the optimal solution? 9. Define shadow price (or dual value). 10. Explain how to use the iso-cost line in a graphical minimiza- tion problem. 11. Compare how the corner-point and iso-profit line methods work for solving graphical problems. 12. Where a constraint crosses the vertical or horizontal axis, the quantity is fairly obvious. How does one go about finding the quantity coordinates where two constraints cross, not at an axis? 13. Suppose a linear programming (maximation) problem has been solved and that the optimal value of the objective func- tion is $300. Suppose an additional constraint is added to this problem. Explain how this might affect each of the following: a) The feasible region. b) The optimal value of the objective function.