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- Consider the following linear programming model: Max 2X1 + 3X2 Subject to: X1 ≤ 2 X2 ≤ 3 X1 ≤ 1 X1, X2 ≥ 0 This linear programming model has: a. alternate optimal solutions b. infeasible solution c. redundant constraint d. unbounded solution8. 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.7. The valid questions for Dynamic Programming are 1) Principle of Optimality (Optimal Substructure), and 2) the condition of insufficient Overlapping Subproblems. Take the example of All-Pairs Shortest Paths as an example to illustrate the problem of satisfying these two conditions.
- In regards of the problem:max cTx subject to Ax = b, with an optimal solution of value v. Suppose the problem min cT x, subject to Ax = b have great with the same value, v. It can be concluded that there is a singlegood point for both? How is the feasible region geometrically?If the optimal solution of a linear programming problem with two constraints is x=5, y=0, s1=3 and s2=0 , then the basic variables are ____.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 optimal
- A pig weighting 200 pounds gains 5 pounds per day and costs 45 cents aday to keep. The market price for pigs is 65 cents per pound, but is falling 1 cent perday.a/ When should the pig be sold? What is the optimal profit?b/ What are the sensitivities of the optimal time and optimal profit with respect to the45-cent upcost?c/ What are the sensitivities of the optimal time and optimal profit with respect to the1-cent market depreciation?Give 2 examples of the optimization problem and identify the following for each problem: Objective Function Design Variable ConstraintThe tableau is not optimal for either maximization or a minimization problem. Thus, when a nonbasic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering nonbasic variable. Basic Z 0 -5 0 4 -1 -10 0 0 598 0 3 0 -2 -3 -1 5 1 12 0 1 1 3 1 0 3 0 6 1 -1 0 0 6 -4 0 0 0 Categorize the variables as basic and nonbasic and provide the current values of all the variables. AP [8] Assuming that the problem is of the maximization type, identify the nonbasic variables that have the potential to improve the value of If each such variable enters the basic solution, determine the associated leaving…