Explanation Given Information: Profit function P ( x ) = 1.3 x − 0.01 x 2 − 30 …… (1) Formula Used: The vertex point is x = − b 2 a where b is the coefficient of x and a is the coefficient of x 2 . The formula of the profit function is, P ( x ) = R ( x ) − C ( x ) , The general profit function P ( x ) = a x 2 + b x + c . Break-even point is the point, when profit is zero or revenue is equal to the cost. Zero product property: The General form of quadratic equation is a x 2 + b x + c = 0 where a , b , c are constants and a ≠ 0 . For real numbers a and b , a b = 0 if and only if a = 0 or b = 0 or both. Calculation: To find the value of maximum profit, compare the equation (1) with the general profit function. Substitute 1.3 for b and − 0.01 for a in the formula of vertex point. x = − 1.3 2 × ( − 0.01 ) = 1.3 0.02 = 65 Substitute 65 for x in the equation P ( x ) = 1.3 x − 0.01 x 2 − 30 to get the maximum profit. P ( 65 ) = 1.3 ( 65 ) − 0.01 ( 65 ) 2 − 30 = 84.5 − 42.25 − 30 = 12

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ISBN: 8220106720264

Author: Reynolds

Publisher: Cengage Learning US

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Chapter 2, Problem 60RE

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To calculate: The maximum profit and break-even point for the function P(x)=1.3x−0.01x2−30. Also, sketch the graph.

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Chapter 2, Problem 59RE

Chapter 2, Problem 61RE

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The maximum profit and break-even point for the function P ( x ) = 1.3 x − 0.01 x 2 − 30 . Also, sketch the graph.

Solution Summary: The author calculates the maximum profit and break-even points for the function P(x)=1.3x-0.01x 2-30.

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To calculate: The maximum profit and break-even point for the function P(x)=1.3x−0.01x2−30. Also, sketch the graph.

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Chapter 2 Solutions