Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y- shaped configuation. Centerville is located at (7, 0) in the xy-plane, Springfield is at (0, 5), and Shelbyville is at (0, The cable runs from Centerville to some point (x, 0) on 5). the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of : f(x) = Preview We find that f(x) has a critical number at x = Preview To verify that f (x) has a minimum at this critical number we compute the second derivative f''(x) and find that its value at the critical number is Preview a positive number. Thus the minimum length of cable needed is Preview A baseball team plays in a stadium that holds 44000 spectators. With the ticket price at $9 the average attendence has been 19000. When the price dropped to $6, the average attendence rose to 22000. Assume that attendence is linearly related to ticket price. What ticket price would maximize revenue? $ Preview
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of cable by arranging the cable in a Y- shaped configuation. Centerville is located at (7, 0) in the xy-plane, Springfield is at (0, 5), and Shelbyville is at (0, The cable runs from Centerville to some point (x, 0) on 5). the x-axis where it splits into two branches going to Springfield and Shelbyville. Find the location (x, 0) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer. To solve this problem we need to minimize the following function of : f(x) = Preview We find that f(x) has a critical number at x = Preview To verify that f (x) has a minimum at this critical number we compute the second derivative f''(x) and find that its value at the critical number is Preview a positive number. Thus the minimum length of cable needed is Preview A baseball team plays in a stadium that holds 44000 spectators. With the ticket price at $9 the average attendence has been 19000. When the price dropped to $6, the average attendence rose to 22000. Assume that attendence is linearly related to ticket price. What ticket price would maximize revenue? $ Preview
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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Question
Transcribed Image Text:Centerville is the headquarters of Greedy Cablevision
Inc. The cable company is about to expand service to two
nearby towns, Springfield and Shelbyville. There needs to
be cable connecting Centerville to both towns. The idea is
to save on the cost of cable by arranging the cable in a Y-
shaped configuation.
Centerville is located at (7, 0) in the xy-plane,
Springfield is at (0, 5), and Shelbyville is at (0,
The cable runs from Centerville to some point (x, 0) on
5).
the x-axis where it splits into two branches going to
Springfield and Shelbyville. Find the location (x, 0) that
will minimize the amount of cable between the 3 towns
and compute the amount of cable needed. Justify your
answer.
To solve this problem we need to minimize the following
function of :
f(x) =
Preview
We find that f(x) has a critical number at x =
Preview
To verify that f (x) has a minimum at this critical number
we compute the second derivative f''(x) and find that its
value at the critical number is
Preview
a positive number.
Thus the minimum length of cable needed is
Preview
Transcribed Image Text:A baseball team plays in a stadium that holds 44000
spectators. With the ticket price at $9 the average
attendence has been 19000. When the price dropped to
$6, the average attendence rose to 22000. Assume that
attendence is linearly related to ticket price.
What ticket price would maximize revenue? $
Preview
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