Explanation Definition used: “ Total Differential: Let z = f ( x , y ) defines a differentiable function of x and y . 1. The differential of the independent variables x, y and z are d x = Δ x , and d y = Δ y . 2. The differential of the dependent variable z is d z = ∂ f ∂ x d x + ∂ f ∂ y d y . Calculation: The model for the monthly profit of Bond and Barker departmental store is given by P ( x , y ) = − 0.02 x 2 − 15 y 2 + x y + 39 x + 25 y − 20000 where x is the level of inventory in thousands of dollars and y is the floor space in thousands of square feet. Given that the level of inventory is $4,000,000 and it is increases by $500,000. Also the floor space is 150,000 ft 2 and it is decreases by 10,000 ft 2 . That is, x = 4000 , d x = 500 , y = 150 , d y = − 10 . The anticipated change can be obtained by computing the total differential of P . Differentiate the equation P ( x , y ) = − 0.02 x 2 − 15 y 2 + x y + 39 x + 25 y − 20000 partially with respect to x as follows. P ( x , y ) = − 0.02 x 2 − 15 y 2 + x y + 39 x + 25 y − 20000 ∂ P ∂ x = ∂ ∂ x ( − 0.02 x 2 − 15 y 2 + x y + 39 x + 25 y − 20000 ) ∂ P ∂ x = − 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 8.6, Problem 31E

To determine

The anticipated change in monthly profit of Bond and Barker departmental store.

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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. 30E Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 38E Ch. 8.5 - Prob. 39E Ch. 8.5 - Prob. 40E Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.6 - Prob. 1CQ Ch. 8.6 - Prob. 2CQ Ch. 8.6 - Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - In Exercises 318, find the total differential of...Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Prob. 24E Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.6 - Prob. 35E Ch. 8.6 - Prob. 36E Ch. 8.6 - Prob. 37E Ch. 8.6 - 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Prob. 5E Ch. 8.8 - Prob. 6E Ch. 8.8 - Prob. 7E Ch. 8.8 - Prob. 8E Ch. 8.8 - Prob. 9E Ch. 8.8 - Prob. 10E Ch. 8.8 - Prob. 11E Ch. 8.8 - Prob. 12E Ch. 8.8 - Prob. 13E Ch. 8.8 - Prob. 14E Ch. 8.8 - Prob. 15E Ch. 8.8 - Prob. 16E Ch. 8.8 - Prob. 17E Ch. 8.8 - Prob. 18E Ch. 8.8 - Prob. 19E Ch. 8.8 - Prob. 20E Ch. 8.8 - Prob. 21E Ch. 8.8 - Prob. 22E Ch. 8.8 - Prob. 23E Ch. 8.8 - Prob. 24E Ch. 8.8 - Prob. 25E Ch. 8.8 - Prob. 26E Ch. 8.8 - Prob. 27E Ch. 8.8 - Prob. 28E Ch. 8.8 - Prob. 29E Ch. 8 - Prob. 1CRQ Ch. 8 - Prob. 2CRQ Ch. 8 - Prob. 3CRQ Ch. 8 - Prob. 4CRQ Ch. 8 - Prob. 5CRQ Ch. 8 - Prob. 6CRQ Ch. 8 - Prob. 7CRQ Ch. 8 - Prob. 8CRQ Ch. 8 - Prob. 9CRQ Ch. 8 - Prob. 10CRQ Ch. 8 - Prob. 11CRQ Ch. 8 - Prob. 12CRQ Ch. 8 - Prob. 13CRQ Ch. 8 - Prob. 1RE Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE Ch. 8 - Prob. 5RE Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - 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The anticipated change in monthly profit of Bond and Barker departmental store.

Solution Summary: The author explains how the anticipated change in monthly profit of Bond and Barker departmental store can be obtained by computing the total differential of P.

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The anticipated change in monthly profit of Bond and Barker departmental store.

Chapter 8 Solutions