Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 4.7, Problem 6P
Explanation of Solution
Basic solutions not being optimal
- Any other basic solution will have s1 and/or s2 as a basic variable.
- Since no right hand side is 0, if s1 or s2 is pivoted in it will be positive...
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The 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…
Isn't the actual optimal S->B->G. If yes, then how are the assumed heuristics valid?
1. Consider an instance of the Knapsack Problem without repetitions with 4 items, having
weights and values as follows. The weights (in pounds) are w1=2, w2 =7, w3 =10, w4 =12.
The dollar values of these items are respectively v1 = 12, v2 = 28, v3 = 30, v4 = 5. The
capacity of the knapsack is 12.
(a) Find the optimal solution for Fractional Knapsack.
(b) Find the optimal solution for 0-1 Knapsack.
Chapter 4 Solutions
Operations Research : Applications and Algorithms
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 6PCh. 4.4 - Prob. 7P
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- In an optimal A* search, a- describe the problem of a heuristic function that overestimates the cost. How does it effect the solution? Give an example. b-is a heuristic method that underestimates the cost admissible? How does it effect the solution? Give an examplearrow_forwardQ 2: f(n) = g(n) + h(n). Discuss which thing should be optimal, underestimated, overestimated, admissible or non-admissible. What will happen if you make it monotonic? Give the example case to preserve its admissibility?arrow_forwardSuppose 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?arrow_forward
- Consider the following initial simplex tableau below, for a maximization LP problem. Interpret, deduce and construct the LP model for this set up. Basic Z 1 -1 -3 0 0 0 0 0 0 3 2 1 0 0 0 10 0 4 1 0 1 0 0 8 0 5 6 0 0 1 0 20 0 2 7 0 0 0 1 30arrow_forwardConsider the following 0-1 knapsack problem, the items, their weights and their profits appear in table below. If the knapsack has capacity 11 select the items that appear in the solution? i.e. select answers 1, 2,and 3 if those are the items in the optimal knapsack. Item 2 3 5 6 Weight 1 2 3 4 5 6 Profit 10 13 15 U item 1 U item 2 U item 3 U item 4 U item 5 U item 6 O O O O O Oarrow_forwardA person is cutting a long board of wood into different length of pieces . Each cutting has fixed width 2 cm lengths. Given that each cutting with different length has a different price, Now, we are required to help this person to find the optimal cuts in order to increase his income. Consider following example showing different cut’s lengths and their equivalent prices. Input: board length = 4 Length [ ] = [1, 2, 3, 4, 5, 6, 7, 8] Price [ ] = [2, 6, 8, 10, 14, 17, 19, 20] Output: Best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12 [Explanation: the possible cuts and profit of each is as follows: As noted the best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12arrow_forward
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