A variable that assumes an optimal value between its lower and upper bounds has a reduced cost value of zero. Why must this be true? (Hint: What if such a variable’s reduced cost value is not zero? What does this imply about the value of the objective function?)
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A variable that assumes an optimal value between its lower and upper bounds has a reduced cost value of zero. Why must this be true? (Hint: What if such a variable’s reduced cost value is not zero? What does this imply about the value of the objective function?)
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- Which of the following statements are true given A* (admissibility and consistency of heuristics ] ? The heuristic function h[n] is called admissible if h[n] is never larger than h*[n], namely h[n] is always less or equal to true cheapest cost from n to the goal. If the heuristic function, h always underestimates the true cost [h[n] is smaller than h*[n]), then A* is guaranteed to find an optimal solution. When h is inconsistent, it can not be admissible. If h is consistent and h[goal)=0 then h is admissible A* is complete and optimalIf an optimal solution to a problem can be obtained by greedy, It can also be obtained by dynamic programming. True or False?The term nonnegativity refers to the condition in which the a. objective function cannot be less than zero. b. decision variables cannot be less than zero. c. right hand side of the constraints cannot be greater than zero. d. reduced cost cannot be less than zero.
- What role does the discount factor play in the Bellman equation, and how does it impact the computation of optimal values?Is it possible to explain how dynamic programming uses the idea of optimality?8. Which of the following statements about linear programming is FALSE? Select one: a. If the change of the objective coefficient is out of the range of optimality, the optimal solution in terms of decision variables will usually change. b. A redundant constraint is also a non-binding constraint. c. In sensitivity analysis of LP problem, if the resource has been used up, the shadow price would be non-zero. d. A difference between minimization and maximization problems is that minimization problems often have unbounded regions. e. If the RHS of a constraint changes in a profit maximization problem, the iso-profit line will change as well.
- What is the principal of optimality ? Explain it's significanceSuppose the risk index for the stock fund (the value of ) increases from its current value of 8 to 12. How does the optimal solution change, if at all? Suppose the risk index for the money market fund (the value of ) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all? Suppose increases to 12 and increases to 3.5. How does the optimal solution change, if at all?Explain the relationship between the Bellman equation and the principle of optimality in dynamic programming.
- If it is possible to create an optimal solution for a problem by constructing optimal solutions for its subproblems, then the problem possesses the corresponding property. a) Subproblems which overlap b) Optimal substructure c) Memorization d) GreedyA blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. The supply and demand for donated blood is shown in the figure along with the unit cost of shipping along each possible arc. Provide the complete linear programing formulation. Clearly specify decision variables, objective function and constraints. Build a model in Excel and paste a screenshot here. Use “FORMULATEXT” in your model to show calculations. According to Excel Solver, what is the optimal transportation plan for blood bank? What is the minimum total shipping cost?A mathematical model that solely gives a representation of the real problem is the only one for which an optimal solution is optimal. True False: O