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(Duality Gap of the Knapsack Problem) Given objects i = 1,...,n with positive weights wi and values vi, we want to assemble a subset of the objects so that the sum of the weights of the subset does not exceed a given T > 0, and the sum of the values of the subset is maximized. This is the knapsack problem, which is a special case of a generalized assignment problem
so that the relative value of the duality gap tends to 0 as k → ∞. Note: This exercise illustrates a generic property of many separable problems with integer constraints: as the number of variables increases, the duality gap decreases in relative terms (see Bertsekas [1982], Section 5.5, or Bertsekas [1995b], Section 5.1, for an analysis and a geometrical interpretation of this phenomenon).
Consider a large population with a mean of 170 and standard deviation of 25. A random sample of size 36 is taken from the population. Calculate the standard error of the sampling distribution of this sample mean and round your answer to the hundre..
1. the daily flow rate of contaminant from an industrial plant is modeled by a normal random variable with a mean value
Suppose that 40% of cars in your area are manufactured in the United States, 30% in Japan, 10% in Germany, and 20% in other countries. If you randomly select 6 cars, what is the probability that two of them are Japanese?
The Kenton Food Company is interested in testing which size of a new organic, whole-grain breakfast cereal is most appealing to consumers. What is being informally tested here, and what is the hypothesis test
Find the range, standard deviation, and variance for the scores.
Compute and compare the proportions of positive cases for the two exposure levels. What would be your conclusion? Calculate the odds ratio associated with high exposure. Does this result support your conclusion in part (a)?
If A is the event that the democratic candidate wins the presidential election in 2012 and B is the event that there is a 6.2 or higher earthquake in Los Angeles sometime in 2013, what would you take as the probability that both A and B occur? Wha..
Twenty defective products are found after a long working day. What is the probability that all the defective products can be reworked?
Determine the values on the 3-sided die so that the outcome probabilities for rolling the two dice described above match exactly the outcome probablities for rolling two standard (6-sided) dice.
a bag contains 3 red marbles 4 green ones 1 lavender one 3 yellows and 2 orange marbleshow many sets of five marbles
according to the uw madison 2003-2004 factbook 11488 of the 24890 students enrolled at uw madison during that year were
A projectile is fired from the platform at B. The shooter fires his gun from point A at an angle 30° of . Determine the muzzle speed of the bullet if it hits the projectile at C
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