Maximizing profit Suppose a tour guide has a bus that holds amaximum of 100 people. Assume his profit (in dollars) for taking npeople on a city tour is P(n) = n(50 – 0.5n) – 100. (Although Pis defined only for positive integers, treat it as a continuous function.)a. How many people should the guide take on a tour to maximizethe profit?b. Suppose the bus holds a maximum of 45 people. How manypeople should be taken on a tour to maximize the profit?

Answered: Image /qna-images/answer/1071b5e9-544e-4509-91d8-bf064a777cc8.jpg

Answered: Maximizing profit Suppose a tour guide…

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 salesperson makes a base salary of $50, 000 a year plus 4% commission on all sales up to (and including) $275, 000 If they exceed $275, 000 in sales for a calendar year, the salesperson's commission jumps to 8% for all their remaining sales over $275, 000 . The salesperson's total salary S for a given year is based on their total sales X . Write the piecewise-defined function S(x). hint: do not forget to include the base salary of $50, 000 when finding the pieces of the function if x 275, 000 .04x+50000 S(x) = { .08x+20000 The submission, .08x+20000, is incorrect.
Example 3. The solid waste generated in the cities of the US, W (in millions of tons), was 238 in 2000 and 250 in 2012. (a) Assuming W increases linearly, write a formula for W as a function of the year t. (b) Find and interpret both the slope and vertical intercept of W (t).
Coal Consumption The following table gives the amount of coal (in thousand short tons) consumed by U. S. utilities to pro- duce electricity. Source: U.S. Department of Energy. Year Consumption 1995 850 2000 986 2005 1037 2010 934 2012 825 (a) Plot the data by letting t be the years since 1990. Would a linear or quadratic function model these data best? (b) Find the quadratic function defined by f(t) = a(t – h)? + k that models the data. Use the highest point as the vertex, (h, k). Then choose (10, 986) as a second point to determine a.
K The manufacturer's suggested retail price (MSRP) for a particular car is $25,275, and it is expected to be worth $14,427 in 4 years. (a) Find a linear depreciation function for this car. (b) Estimate the value of the car 5 years from now. (c) At what rate is the car depreciating? (a) What is the linear depreciation function for this car? f(x) = (Simplify your answer. Do not include the $ symbol in your answer.) (b) What is the estimated value of the car 5 years from now? (c) At what rate is the car depreciating? The car is decreasing in value an average of $ a year.
Find a and b.
5. Find the maximum or minimum of the function, and state whether your answer is a maximum or minimum. i. f(x) = 6x² – 36x – 100

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