Explanation Given Information: The owner of small boutique can sell x = 300 pairs of earrings per month at the rate of p = $ 15 per pair. 375 pairs of earrings per month are actually sold at the price of $ 12 per pair. The fixed monthly costs are $ 530 and the supplies needed to produce the earrings cost $ 2.20 per pair. Formula used: If the relationship between the dependent variable y and independent variable x is linear of the form y = m x + c , then given two points A ( x 1 , y 1 ) and B ( x 2 , y 2 ) , the equation of the line in two point form is y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) Where y 2 − y 1 x 2 − x 1 = m is the slope. The distributive property over addition and subtraction for any real numbers a , b , c a ⋅ ( b + c ) = a ⋅ b + a ⋅ c a ⋅ ( b − c ) = a ⋅ b − a ⋅ c The total cost function C is the sum of fixed cost and variable cost for all the items. C = Total cost + Variable Cost The profit P is P = R − C . Calculation: Consider the provided information, The owner of small boutique can sell x = 300 pairs of earrings per month at the rate of p = $ 15 per pair. 375 pairs of earrings per month are actually sold at the price of $ 12 per pair. The fixed monthly costs are $ 530 and the supplies needed to produce the earrings cost $ 2.20 per pair. The independent variable x is the earrings sold and the dependent variable p is the price. The ordered pairs ( x , p ) are ( 300 , 15 ) and ( 375 , 12 ) . Now, substitute the values ( 300 , 15 ) and ( 375 , 12 ) in the slope formula y 2 − y 1 x 2 − x 1 = m . Therefore, m = 12 − 15 375 − 300 = − 3 75 = − 0.04 Now, substitute the slope m = − 0

1st Edition

ISBN: 9781259218859

Author: David Sobecki Professor, Brian A. Mercer

Publisher: McGraw-Hill Education

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Chapter 4.7, Problem 9G

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To calculate: The number of earrings to give largest possible profit P on selling earrings using trial and error if x=300 pairs of earrings per month can be sold at the rate of p=$15 per pair. 375 pairs of earrings per month are actually sold at the price of $12 per pair.

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Chapter 4.7, Problem 8G

Chapter 4.7, Problem 10G

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The number of earrings to give largest possible profit P on selling earrings using trial and error if x = 300 pairs of earrings per month can be sold at the rate of p = $ 15 per pair. 375 pairs of earrings per month are actually sold at the price of $ 12 per pair.

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To calculate: The number of earrings to give largest possible profit P on selling earrings using trial and error if x=300 pairs of earrings per month can be sold at the rate of p=$15 per pair. 375 pairs of earrings per month are actually sold at the price of $12 per pair.

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