Answered: 2 (a) Find a quadratic function for the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

A street vendor constructs the table below on the basis of sales data. (Note: Consumer expenditure and revenue are terms for the same thing from different perspectives. Consumer expenditure is the amount of money that consumers spend on a product, and revenue is the amount of money that businesses take in by selling the product.)

Sales of Roses, Given the Price per Dozen

Price (dollars)	Sales (dozen roses)
20	167
25	157
30	132
32	92

(a) Find a quadratic function for the model of the data that gives the quantity sold at x dollars, data from

20 ≤ x ≤ 32. (Round all numerical values to three decimal places.)

S(x) ≈

(b) Find a function for the model for consumer expenditure (revenue for the vendor), where x is the price in dollars, data from 20 ≤ x ≤ 32. (Round all numerical values to three decimal places.)

R(x) ≈

(c) What price should the street vendor charge to maximize consumer expenditure? (Round your answer to two decimal places.)
$ ____

(d) If each dozen roses costs the vendor $14, what price should he charge to maximize his profit? (Round your answer to two decimal places.)
$ ____

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