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(Constraint Relaxation and Lagrangian Relaxation) The purpose of this exercise is to compare the lower bounds obtained by relaxing integer constraints and by dualizing the side constraints. Consider the nonlinear network optimization problem with a cost function f(x), the conservation of flow constraints, and the additional constraint
where Xij are given subsets of the real line and the functions gt are linear. We assume that f is convex over the entire space of flow vectors x. We introduce a Lagrange multiplier µt for each of the side constraints gt(x) ≤ 0, and we form the corresponding Lagrangian function
\
Cars pass a certain street location according to a Poisson process with rate λ. A woman who want to cross the street at that location waits until she can see that no cars will come by in the next T time units.
Draw a model of the relation {(-6,-8), (3,-3), (-6,-7), (9,7)}. Is the relation a function? Why or why not? Evaluate the function at the specified values of the independent variable and simplify.
Suppose you purchase two microwaves that were produced at the same factory, which is equally likely to have been either factory A or factory B. If the first microwave that you check is defective, what is the conditional probability that the other ..
a well-insulated rigid tank of volume 10 ft3 contains carbon dioxide initially at 30 psia and 60 degrees f. the tank is
If 2 randomly chosen students are surveyed and both feel optimistic about their employment prospects, what is the probability that both were math students?
bp cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year. the
Give a point estimate for the mean amount per customer spent at the supermarket and give a 99% confidence interval estimate for the mean amount per customer spent at the supermarket.
during ejection from a military airplane the pilots acceleration must not exceed 16g ig injury is to be avoided.
a. Compute the mean and standard deviation of x. b. Compute the mean and standard deviation of y. c. Compute the mean and variance of the total amount of money collected in tolls from cars.
1. For the period 1998-2008, McDonald's Corporation paid the following dividends (rounded to nearest penny) per share of common stock. Source: McDonald's Corporation, 2005 Annual Report, p. 1; 2008 Annual Report, p. 19.
art, French, and mathematics. He chooses art with probability 5/8, French with probability 5/8, and art and French together with probability 1/4. What is the probability that he chooses mathematics?
A sample of n=20 has a mean of M=40. If the standard deviation is s=5, would a score of x=55 be considered an extreme value?
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