2 (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.) $
2 (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.) $
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 46E
Related questions
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
(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.)
(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.)
$ ____
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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