 7.7.1: Consider the following linear program.maximize 5x + 3y5x 2y 0x + y ...
 7.7.2: Duckwheat is produced in Kansas and Mexico and consumed in New York...
 7.7.3: A cargo plane can carry a maximum weight of 100 tons and a maximum ...
 7.7.4: Moe is deciding how much Regular Duff beer and how much Duff Strong...
 7.7.5: The Canine Products company offers two dog foods, Frisky Pup and Hu...
 7.7.6: Give an example of a linear program in two variables whose feasible...
 7.7.7: Find necessary and sufficient conditions on the reals a and b under...
 7.7.8: You are given the following points in the plane:(1, 3), (2, 5), (3,...
 7.7.9: A quadratic programming problem seeks to maximize a quadratric obje...
 7.7.10: For the following network, with edge capacities as shown, find the ...
 7.7.11: Write the dual to the following linear program.max x + y2x + y 3x +...
 7.7.12: For the linear programmax x1 2x3x1 x2 12x2 x3 1x1, x2, x3 0prove th...
 7.7.13: Matching pennies. In this simple twoplayer game, the players (call...
 7.7.14: The pizza business in Little Town is split between two rivals, Tony...
 7.7.15: Find the value of the game specified by the following payoff matrix...
 7.7.16: A salad is any combination of the following ingredients: (1) tomato...
 7.7.17: Consider the following network (the numbers are edge capacities).(a...
 7.7.18: There are many common variations of the maximum flow problem. Here ...
 7.7.19: Suppose someone presents you with a solution to a maxflow problem ...
 7.7.20: Consider the following generalization of the maximum flow problem.Y...
 7.7.21: An edge of a flow network is called critical if decreasing the capa...
 7.7.22: In a particular network G = (V, E) whose edges have integer capacit...
 7.7.23: A vertex cover of an undirected graph G = (V, E) is a subset of the...
 7.7.24: Direct bipartite matching. Weve seen how to find a maximum matching...
 7.7.25: The dual of maximum flow. Consider the following network with edge ...
 7.7.26: In a satisfiable system of linear inequalitiesa11x1 + + a1nxn b1......
 7.7.27: Show that the changemaking problem (Exercise 6.17) can be formulat...
 7.7.28: A linear program for shortest path. Suppose we want to compute the ...
 7.7.29: Hollywood. A film producer is seeking actors and investors for his ...
 7.7.30: Halls theorem. Returning to the matchmaking scenario of Section 7.3...
 7.7.31: Consider the following simple network with edge capacities as shown
Solutions for Chapter 7: Linear programming and reductions
Full solutions for Algorithms  1st Edition
ISBN: 9780073523408
Solutions for Chapter 7: Linear programming and reductions
Get Full SolutionsThis textbook survival guide was created for the textbook: Algorithms , edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7: Linear programming and reductions includes 31 full stepbystep solutions. Algorithms was written by and is associated to the ISBN: 9780073523408. Since 31 problems in chapter 7: Linear programming and reductions have been answered, more than 10629 students have viewed full stepbystep solutions from this chapter.

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Average
See Arithmetic mean.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

Chisquare (or chisquared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Conidence level
Another term for the conidence coeficient.

Continuous distribution
A probability distribution for a continuous random variable.

Control limits
See Control chart.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Correlation
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

Dependent variable
The response variable in regression or a designed experiment.

Experiment
A series of tests in which changes are made to the system under study

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

Frequency distribution
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .