Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: • pis the wholesale price (in dollars) of a sleeping bag for a weekly demand of z sleeping bags; C is the total cost (in dollars) of producing z sleeping bags. r (sleeping bags) P ($) C ($) 95 240 13,000 120 235 14,300 180 155 18.500 220 50 21.000 Price Model Find a quadratic regression equation for the price-demand data, using z as the independent variable. p=a+ br + cr? Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places. Revenue Model Using the regression model computed above, find a model for the weekly revenue, using z as the independent variable. NOTE: Do not calculate another regression. Use the price equation to find a model for revenue R(z) =p x. R(z) =p.r (a+ bx + cz²)z ³ = ar + bx? + ca Cost Model Find a linear regression model for the weekly cost data, using a as the independent variable. C(x) = = mx + k Round m to 1 decimal place, and round k to the nearest integer.
Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: • pis the wholesale price (in dollars) of a sleeping bag for a weekly demand of z sleeping bags; C is the total cost (in dollars) of producing z sleeping bags. r (sleeping bags) P ($) C ($) 95 240 13,000 120 235 14,300 180 155 18.500 220 50 21.000 Price Model Find a quadratic regression equation for the price-demand data, using z as the independent variable. p=a+ br + cr? Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places. Revenue Model Using the regression model computed above, find a model for the weekly revenue, using z as the independent variable. NOTE: Do not calculate another regression. Use the price equation to find a model for revenue R(z) =p x. R(z) =p.r (a+ bx + cz²)z ³ = ar + bx? + ca Cost Model Find a linear regression model for the weekly cost data, using a as the independent variable. C(x) = = mx + k Round m to 1 decimal place, and round k to the nearest integer.
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...
Related questions
Question
What is A? What is B?
Transcribed Image Text:Profit Model
Use the models computed to find a model for the weekly profit, using a as the independent variable.
P(x) = r + ux + sx2 + tx3
NOTE: Do not calculate another regression. Use the fact that profit is revenue minus cost.
Round r to the nearest integer, round u to 1 decimal place, round s to 2 decimal places, and round t
to 4 decimal places.
The weekly profit model has roots at a = -52.789, x = 47.555, and x = 202.944, rounded to 3
decimal places.
The marginal weekly profit model has roots at a = -8.488 and x = 140.295, rounded to 3
decimal places.
Yaster Outfitters
• makes a profit on extreme-cold sleeping bags when the weekly production level a satisfies
A < x < B;
• loses money when 0 < æ < A or x > B.
In other words, Yaster starts making a profit when production exceeds A sleeping bags per week,
and starts losing money when production exceeds B sleeping bags per week.
Round A and B to 3 decimal places.
What is B? Round to 3 decimal places.
What is A? Round to 3 decimal places.
sleeping bags
sleeping bags
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Transcribed Image Text:Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the
price-demand and total cost data, where:
. pis the wholesale price (in dollars) of a sleeping bag for a weekly demand of z sleeping bags:
. C is the total cost (in dollars) of producing r sleeping bags.
r (sleeping bags)
p ($)
C ($)
95
240
13,000
120
235
14,300
180
155
18,500
220
50
21.000
Price Model
Find a quadratic regression equation for the price-demand data, using r as the independent variable.
p= a + bx + cr?
Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places.
Revenue Model
Using the regression model computed above, find a model for the weekly revenue, using x as the
independent variable.
NOTE: Do not calculate another regression. Use the price equation to find a model for revenue
R(2) =p-x.
R(x) p.r (a + bx + cz?)x
= ax + bx? + ca³
Cost Model
Find a linear regression model for the weekly cost data, using a as the independent variable.
C(x)
= mx + k
Round m to 1 decimal place, and round k to the nearest integer.
* Accessibility: Investigate
re to search
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