(a) Explanation Given: The profit equation as; Profit = − 10 ( x 2 − 200 x + 1800 ) Formula used: Quadratic formula: The root of the quadratic equation a x 2 + b x + c = 0 is given by; x = − b ± b 2 − 4 a c 2 a Calculation: Find the number of units sold, x when the profit is greater than zero as: Profit > 0 − 10 ( x 2 − 200 x + 1800 ) > 0 Multiply by − 10 will change the inequality; x 2 − 200 x + 1800 < 0 Since, factorization of the given quadratic equation is not possible, use quadratic formula to find the boundary points as: x = − ( − 200 ) ± ( − 200 ) 2 − 4 ( 1 ) ( 1800 ) 2 ( 1 ) = 200 ± 40000 − 7200 2 = 200 ± 32800 2 = 100 ± 90.6 Now, use calculator to find the possible boundary of t as: x = 100 + 90.6 = 190.6 And, x = 100 − 90.6 = 9.4 Divide the number line with the help of this boundary points (b) To determine To calculate: The daily profit when 50 units are sold for the profit function − 10 ( x 2 − 200 x + 1800 ) . (c) To determine To calculate: The daily profit when 60 units are sold for the profit function − 10 ( x 2 − 200 x + 1800 )

Intermediate Algebra Books a la Carte Edition PLUS MyLab Math (8th Edition)

8th Edition

ISBN: 9780134578507

Author: John Tobey Jr., Jeffrey Slater, Jenny Crawford, Jamie Blair

Publisher: PEARSON

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Chapter 8.6, Problem 31E

(a)

To determine

To calculate: The number of units sold, x when the profit given by equation −10(x2−200x+1800) is greater than zero.

(b)

To determine

To calculate: The daily profit when 50 units are sold for the profit function −10(x2−200x+1800).

(c)

To determine

To calculate: The daily profit when 60 units are sold for the profit function −10(x2−200x+1800)

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Chapter 8.6, Problem 30E

Chapter 8.6, Problem 32E

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The number of units sold, x when the profit given by equation − 10 ( x 2 − 200 x + 1800 ) is greater than zero.

Solution Summary: The author calculates the number of units sold, x when the profit given by the quadratic equation is greater than zero.

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To calculate: The number of units sold, x when the profit given by equation −10(x2−200x+1800) is greater than zero.

To calculate: The daily profit when 50 units are sold for the profit function −10(x2−200x+1800).

To calculate: The daily profit when 60 units are sold for the profit function −10(x2−200x+1800)

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Chapter 8 Solutions