3) Jim is selling sweatshirts on the quad. When he sets the price at $28 per sweatshirt, they sell 200sweatshirts each week. For every $1 increase in price per sweatshirt, they will sell 4 fewer sweatshirtsper week.a) Find the revenue function. Clearly identify your variablesRevenueb.) use a method of calculus to maximize the weekly revenue from selling sweatshirts. Determine thenumber of sweatshirts they must sell, the price, and find the maximum revenue. You must verify thatyou did find the maximum. (SHOW all work in the space below)Number of sweatshirtsPrice of the sweatshirt_Verity (test) you need to state thedomain you are using ang test correctly.

Answered: 3) Jim is selling sweatshirts on 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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Similar questions

A contractor purchases a backhoe for $37, 300. Fuel and standard maintenance cost $5.95 per hour, and the operator is paid $12.03 per hour. a. Write a cost function for the cost C(z) of operating the backhoe for hours. Be sure to include the purchase price in the cost function. Cost function: C(z) = dollars b. If customers pay $27.77 per hour for the contractor's backhoe service, write the revenue function R(z) for the amount of revenue gained from a hours of use. Revenue function: R(x) = I c. Write the profit function P(x) for the amount of profit gained from a hours of use. Profit function: P(x) = dollars dollars d. How many hours must the backhoe be used in order to break even (assume that part of an hour counts as a whole hour)? In order for the contractor to break even, customers need to pay to use the backhoe for a total of hours.
A store is having a sale where all items are 16% off. Write an equation to represent the relationship between the sale price of an item, s, and the original price, p, where s and p are in dollars.
It costs a publishing company $60,001 in fixed costs and it costs $4.20 per book to produce them. The publisher sells the books for $10 each. What are the revenue and cost functions? Find and interpret the break-even point.
The owner of an apartment building has 100 apartments. He has found that if he charges $500 per month he can rent all 100 of them but he rents one fewer apartment for each $25 increase in monthly rent. a. Write an equation that gives the monthly revenue from the rental of the apartments if he makes x increases of $25 in the rent. b. Find the rent he should charge to maximize the monthly revenue and the number of apartments he will rent by charging this amount. c. Suppose the landlord pays for water, sewer, and electricity at his apartments for a cost of $50 per apartment per month. Write an equation that gives the monthly cost to the landlord after x price increases of $25. d. Write an equation that gives the monthly profit the landlord makes, and the rent he should charge to maximize his monthly profit, and the number of apartments he will rent by charging this amount. e. Explain why you know mathematically your solutions to (2) and (4) are maximum values. f. In a sentence or two…
A shirt producer has a fixed monthly cost of $3600. If each shirt has a cost of $3 and sells for $12 find: Cost function Revenue function Profit
Find the derivative of y = [A 0 tan Od0. sin x

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