Optimal Chapter-Flight Fare If exactly 218 people sign up for a charter flight, Leisure World Travel Agency charges $310/person. However, if more than 218 people sign up for theflight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency. Hint:Let x denote the number of passengers above 218. Show that the revenue function R is given by R(x) = (218 + x)(310 - x).passengersWhat is the maximum revenue?What would be the fare per passenger in this case?dollars per passenger

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Answered: Öptimal Chapter-Flight Fare If exactly…

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 farmer wishes to build a divided pasture adjacent to the river, as shown in the diagram. Express the total area of the pasture as a function of x if 1000 feet of fencing is available for construction.
A store has issued two different coupons for its customers to use. One coupon gives customers $20 off their purchase price, and the other coupon gives customers 30% off of their purchase. The store allows customers to use both coupons and choose which coupon to apply first. For this context, ignore sales tax. Let ff be the function that inputs a cost (in dollars) and outputs the cost after applying the "$20 off" coupon, and let gg be the function that inputs a cost (in dollars) and outputs the cost after applying the "30% off" coupon. A customer purchases an item for $120 and asks the cashier to apply the "$20 off" coupon first, followed by the "30% off" coupon. What is the cost of the item after the two coupons are applied? $ A customer purchases an item for $120 and asks the cashier to apply the "$20 off" coupon first, followed by the "30% off" coupon. Use function notation to represent the cost of the item (in dollars) after the two coupons are applied. A customer…
According to the postal service in the United States, first class mail is used for personal and business correspondence. Any item that is sent by mail, could be sent first class. Includes postcards, letters, large envelopes, and small packages. Maximum weight is 13 ounces. The following function is used to calculate the cost of mailing a first class letter, where x is the weight of the package in ounces. Calculate the cost in dollars of shipping a package first class for the following weights: A letter weighing 4.3 ounces: ____ dollarsA postcard that weighs 0.4 ounces: ____ dollarsA package weighing 12.2 ounces: ____ dollars
You sell candy at an event to make money. When candy are sold for $1.10 per bag, approximately 625 bags are sold at each event. You tried to raise the price to $1.35 and found that the quantity demanded dropped to 525 bags. The startup cost was $500 and the cost to you per bag of peanuts is $0.50. Assume that the demand function is linear and write a function that models the profit from selling x bags of peanuts at an event. What number of bags and what price per bag will get you a maximum profit?
When the U.S. Environmental Protection Agency found a certain company emitting ozone-depleting substances from refrigeration equipment, it fined the company $600,000, plus $50,000 per month until the company complied with federal emission regulations. Express the total fine as a function of the number of months, x, the company continued to violate the federal regulations.
The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below. Price 0.00 0.45 0.60 0.75 1.00 1.25 1.40 1.50 Profit 0.00 $720 $900 $990 $845 $625 $560 $300 What factors might influence how much is to be made from the candy sale? Give at least two. What happens to the profit as the price of each candy bar increases? Explain possible reasons for your observations. How do you suppose the other bands determined the price at which to sell each candy bar? Do any data values seem unusual? Yes or…
Use function notation to represent that your annual salary after working five years at your job is $2,000 more than your initial salary.

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