a. Explanation Given: The function is D ( x , y ) = 500 e − 0.02 x ( x − 120 ) ( 1 − 0.7 e − 0.0001 y ) . The x and y ranges from 120 ≤ x ≤ 280 , 0 ≤ y ≤ 30 , 000 . Proof: The given function is D ( x , y ) = 500 e − 0.02 x ( x − 120 ) ( 1 − 0.7 e − 0.0001 y ) . Compute the partial derivative of D ( x , y ) with respect to x . D x ( x , y ) = 500 ∂ ∂ x ( e − 0.02 x ( x − 120 ) ( 1 − 0.7 e − 0.0001 y ) ) = 500 [ ( 1 − 0.7 e − 0.0001 y ) ∂ ∂ x ( e − 0.02 x ( x − 120 ) ) ] = 500 ( 1 − 0.7 e − 0.0001 y ) ( − ( e − 0.02 x ( x − 120 ) ) ) ∂ ∂ x ( 0.002 x ( x − 120 ) ) Simplify further as follows, D x ( x , y ) = 500 ( 1 − 0.7 e − 0.0001 y ) ( − ( e − 0.02 x ( x − 120 ) ) ) ∂ ∂ x ( 0.002 x ( x − 120 ) ) = − 500 ( 1 − 0.7 e − 0 (b). To determine To find: The approximate change in the demand for the number of rooms, if the daily room rate is cut by $1 from the current $200/night.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

10th Edition

ISBN: 9781285464640

Author: Soo T. Tan

Publisher: Brooks Cole

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 8.2, Problem 50E

To determine

To show: When y is held fast, D is a decreasing function of x and if x is held fast, D is an increasing function of y and interpret the result.

(b).

To determine

To find: The approximate change in the demand for the number of rooms, if the daily room rate is cut by $1 from the current $200/night.

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Chapter 8.2, Problem 49E

Chapter 8.2, Problem 51E

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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Ch. 8.1 - What is a function of two variables? Give an...Ch. 8.1 - If f is a function of two variables, what can you...Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Let g(x, y) = 2x2 y2. Compute g(1, 2), g(2,1),...Ch. 8.1 - Prob. 3E 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 - Prob. 9E 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 - Prob. 15E 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 - In Exercises 19-24, sketch the level curves of the...Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - In Exercises 19-24, 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 - In Exercises 27 and 28, match the graph of the...Ch. 8.1 - Prob. 28E Ch. 8.1 - Can two level curves of a function f of two...Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - PRICE-TO-EARNINGS Ratio The current PE ratio...Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - COST FUNCTION FOR A LOUDSPEAKER SYSTEM Acrosonic...Ch. 8.1 - REVENUE FUNCTION FOR ELECTRIC CARS Bell Motors...Ch. 8.1 - 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Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.6 - Prob. 1CQ Ch. 8.6 - Prob. 2CQ Ch. 8.6 - Prob. 3CQ Ch. 8.6 - Prob. 4CQ Ch. 8.6 - Prob. 5CQ 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 - In Exercises 1-25. evaluate the double integral...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 - Prob. 15E 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 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - In Exercises 26-33, use a double integral to find...Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.6 - Prob. 35E Ch. 8.6 - Prob. 36E Ch. 8.6 - 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When y is held fast, D is a decreasing function of x and if x is held fast, D is an increasing function of y and interpret the result.

Solution Summary: The author explains that when y is held fast, D is a decreasing function of x and if it is an increasing function. Compute the partial derivative of D(x,y) with