Explanation Given: Inequalities are as follows: 2 x 1 + 3 x 2 ≤ 8 (I) x 1 + 4 x 2 ≥ 7 (II) Explanation: Slack variable is the variable that is added to less than or equal to ( ≤ ) type inequality in order to get a constraint. The surplus variable is the variable that is added to greater than or equal to ( ≥ ) type inequality in order to get a constraint. The surplus variable is also known as a negative slack variable. Add slack variable (say s 1 ) to equation (I). As a result, 2 x 1 + 3 x 2 + s 1 = 8 Now, add a surplus variable (say − s 2 ) to equation (II)

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 4.4, Problem 1E

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To rewrite: Each system of inequalities as a system of linear equations by adding slack variable or by subtracting surplus variable.

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Chapter 4.3, Problem 29E

Chapter 4.4, Problem 2E

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Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output: Estimate SE Z Pr(>|Z|) (Intercept) -0.8161 0.086 -9.4895 0 to_multiple -2.5651 0.3052 -8.4047 0 winner 1.5801 0.3156 5.0067 0 format -0.1528 0.1136 -1.3451 0.1786 re_subj -2.8401 0.363 -7.824 0 (a) Write down the model using the coefficients from the model fit.log_odds(spam) = -0.8161 + -2.5651 + to_multiple + 1.5801 winner + -0.1528 format + -2.8401 re_subj(b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?…

Chapter 4 Solutions

Finite Mathematics (11th Edition)

Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4E Ch. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...

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To rewrite: Each system of inequalities as a system of linear equations by adding slack variable or by subtracting surplus variable.

Solution Summary: The author explains that each system of inequalities is a linear equation by adding slack variable or by subtracting surplus variable.

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To rewrite: Each system of inequalities as a system of linear equations by adding slack variable or by subtracting surplus variable.

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Chapter 4 Solutions