Explanation Given: The total profit of publishing and selling the dictionary is given by P ( x , y ) = − 0.005 x 2 − 0.003 y 2 − 0.002 x y + 14 x + 12 y − 200 . The target for the publish management for a day is 400 copies. Calculation: It is given that the deluxe editions and the standard editions publication is exactly 400 each day. That is, x + y = 400 . Obtain the maximized value of the equation P ( x , y ) = − 0.005 x 2 − 0.003 y 2 − 0.002 x y + 14 x + 12 y − 200 subjected to a constraint of function g ( x , y ) = x + y − 400 . Frame an auxiliary function P for the given function P ( x , y ) subject to g ( x , y ) = 0 . F ( x , y , λ ) = P ( x , y ) + λ g ( x , y ) = − 0.005 x 2 − 0.003 y 2 − 0.002 x y + 14 x + 12 y − 200 + λ ( x + y − 400 ) The above expression is called the Lagrange function while λ be the Lagrange multipliers. Differentiate F ( x , y , λ ) = − 0.005 x 2 − 0.003 y 2 − 0.002 x y + 14 x + 12 y − 200 + λ ( x + y − 400 ) with respect to x , d d x ( F ( x , y , λ ) ) = d d x ( − 0.005 x 2 − 0.003 y 2 − 0.002 x y + 14 x + 12 y − 200 + λ ( x + y − 400 ) ) F x = ( d d x ( − 0.005 x 2 − 0.003 y 2 − 0.002 x y + 14 x + 12 y − 200 ) + d d x ( λ ( x + y − 400 ) ) ) = − 0.01 x − 0.002 y + 14 + λ Differentiate F ( x , y , λ ) = − 0.005 x 2 − 0.003 y 2 − 0.002 x y + 14 x + 12 y − 200 + λ ( x + y − 400 ) with respect to y , d d y ( F ( x , y , λ ) ) = d d y ( − 0

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 8.5, Problem 18E

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To find: The number of deluxe copies and standard copies published each day to make maximum profit.

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Chapter 8 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 8.1 - What is a function of two variables? Give an...Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Let f(x, y) = x2+ 2xy x + 3. Compute f(1, 2),...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Let h(s, t) = s ln t t ln s. Compute h(1, e),...

Ch. 8.1 - Prob. 8E Ch. 8.1 - Let g(r, s, t) = res/t. Compute g(1, 1, 1), g(1,...Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 14E Ch. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 16E Ch. 8.1 - In Exercises 11-18, find the domain of the...Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - In Exercises 19-24, sketch the level curves of the...Ch. 8.1 - Prob. 22E Ch. 8.1 - In Exercises 1924, sketch the level curves of the...Ch. 8.1 - Prob. 24E Ch. 8.1 - Find an equation of the level curve of f (x, y) =...Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - POISEITLLES LAW Poiseuilles Law states that the...Ch. 8.1 - COST FUNCTION FOR A LOUDSPEAKER SYSTEM Acrosonic...Ch. 8.1 - Prob. 38E Ch. 8.1 - REVENUE FUNCTIONS FOR DESKS Country Workshop...Ch. 8.1 - Prob. 40E Ch. 8.1 - 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Prob. 1TE Ch. 8.2 - Prob. 2TE Ch. 8.2 - Prob. 3TE Ch. 8.2 - Prob. 4TE Ch. 8.2 - Prob. 5TE Ch. 8.2 - Prob. 6TE Ch. 8.3 - Explain the terms (a) relative maximum of a...Ch. 8.3 - Prob. 2CQ Ch. 8.3 - Prob. 3CQ Ch. 8.3 - Prob. 4CQ Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - In Exercises 1-20, find the critical point(s) of...Ch. 8.3 - In Exercises 1-20, find the critical point(s) of...Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - MAXIMIZATION PROFIT The total weekly revenue (in...Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - MAXIMIZING REVENUE The management of Cal...Ch. 8.3 - Prob. 26E Ch. 8.3 - MAXIMIZING PROFIT Johnsons Household Products has...Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - Prob. 41E Ch. 8.3 - Prob. 42E Ch. 8.4 - Explain the terms (a) scatter diagram and (b)...Ch. 8.4 - Prob. 2CQ Ch. 8.4 - Prob. 4CQ Ch. 8.4 - Prob. 1E Ch. 8.4 - Prob. 2E Ch. 8.4 - In Exercises 16, (a) find an equation of the...Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - COLLEGE ADMISSIONS The following data, compiled by...Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - 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The number of deluxe copies and standard copies published each day to make maximum profit.

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To find: The number of deluxe copies and standard copies published each day to make maximum profit.

Chapter 8 Solutions