A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by p = 60 − 0.03x and C = 4000 + 30x − 0.04x2, where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are x = 800 units.

Given: Demand function is: p=60-0.03x Cost function is: C(x)=4000+30x-0.04x2

Answered: A company is increasing the production…

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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A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by

p = 60 − 0.03x

and

C = 4000 + 30x − 0.04x²,

where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are

x = 800 units.

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