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Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = .007x³ +.02x² + 4x. Currently, Pierce sells 65 lawn chairs daily. a) What is the current daily revenue? b) What is the equation for marginal revenue? c) What is the marginal revenue when x = 65? 9.a) b) c)

Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = .007x³ +.02x² + 4x. Currently, Pierce sells 65 lawn chairs daily. a) What is the current daily revenue? b) What is the equation for marginal revenue? c) What is the marginal revenue when x = 65? 9.a) b) c)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Pierce Manufacturing's Revenue Analysis** Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of \( x \) lawn chairs is represented by the equation: \[ R(x) = 0.007x^3 + 0.02x^2 + 4x. \] Currently, Pierce sells 65 lawn chairs daily. The following questions address the calculation of daily revenue, marginal revenue, and the implications of a change in sales. **a) Current Daily Revenue** - *Question*: What is the current daily revenue? - *Explanation*: Substitute \( x = 65 \) into the revenue equation \( R(x) \) to find the current daily revenue. **b) Equation for Marginal Revenue** - *Question*: What is the equation for marginal revenue? - *Explanation*: Marginal revenue is found by taking the derivative of the revenue function \( R(x) \). **c) Marginal Revenue when \( x = 65 \)** - *Question*: What is the marginal revenue when \( x = 65 \)? - *Explanation*: Substitute \( x = 65 \) into the marginal revenue equation derived in part b to find the specific marginal revenue for 65 lawn chairs. **d) Weekly Revenue Estimation with Increased Sales** - *Question*: Use your answer from part c to estimate the weekly revenue if sales increase to 66 lawn chairs daily. - *Explanation*: The obtained marginal revenue for 65 chairs is used to estimate additional revenue per day when selling 66 chairs. Multiply this by the number of days in a week to find the total change in weekly revenue. Each part of this analysis builds on calculus concepts related to finding revenue functions, derivatives, and using marginal analysis for decision-making.
Transcribed Image Text:**Pierce Manufacturing's Revenue Analysis** Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of \( x \) lawn chairs is represented by the equation: \[ R(x) = 0.007x^3 + 0.02x^2 + 4x. \] Currently, Pierce sells 65 lawn chairs daily. The following questions address the calculation of daily revenue, marginal revenue, and the implications of a change in sales. **a) Current Daily Revenue** - *Question*: What is the current daily revenue? - *Explanation*: Substitute \( x = 65 \) into the revenue equation \( R(x) \) to find the current daily revenue. **b) Equation for Marginal Revenue** - *Question*: What is the equation for marginal revenue? - *Explanation*: Marginal revenue is found by taking the derivative of the revenue function \( R(x) \). **c) Marginal Revenue when \( x = 65 \)** - *Question*: What is the marginal revenue when \( x = 65 \)? - *Explanation*: Substitute \( x = 65 \) into the marginal revenue equation derived in part b to find the specific marginal revenue for 65 lawn chairs. **d) Weekly Revenue Estimation with Increased Sales** - *Question*: Use your answer from part c to estimate the weekly revenue if sales increase to 66 lawn chairs daily. - *Explanation*: The obtained marginal revenue for 65 chairs is used to estimate additional revenue per day when selling 66 chairs. Multiply this by the number of days in a week to find the total change in weekly revenue. Each part of this analysis builds on calculus concepts related to finding revenue functions, derivatives, and using marginal analysis for decision-making.
Expert Solution
Step 1: Introduction

Since you have posted a question with multiple subparts, we will solve only the first three subparts of the question. Kindly repost the others in the next question.

Given:

The daily revenue from the sale of x lawn chairs is given by the function R open parentheses x close parentheses equals 0.007 x cubed plus 0.02 x squared plus 0.4 x, where the daily revenue is in dollars.

Also, given that currently, the total quantity of lawn chairs sold daily by Pierce is 65.

To Find:

We have to determine,

a) the current daily revenue

b) the equation for marginal revenue

c) the marginal revenue when x equals 65

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