What is the maximum weekly profit? What is the wholesale price per sleeping bag that should be charged to realize the maximum weekly profit? Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows theprice-demand and total cost data, where:• p is the wholesale price (in dollars) of a sleeping bag for a weekly demand of r sleeping bags;. Cis the total cost (in dollars) of producing r sleeping bags.a(sleeping bags)p ($)C ($)9524013,00012023514,30018015518,5002205021.000Price ModelFind a quadratic regression equation for the price-demand data, using z as the independent variable.p = a + bx + czRound a to the nearest integeround b to 2 decimal places, and round e to 4 decimal places.Revenue ModelUsing the regression model computed above, find a model for the weekly revenue, using a as theindependent variable.NOTE: Do not calculate another regression. Use the price equation to find a model for revenueR(z) = p.r.R(z) = p.r=(a+ bz + cx?)r ax + bx? + cz³Cost ModelFind a linear regression model for the weekly cost data, using a as the independent variable.C(x) = mx +kRound m to 1 decimal place, and round k to the nearest integer.* Accessibility:. Investigatenere to searchN Profit ModelUse the models computed to find a model for the weekly profit, using a as the independent variable.P(x) = r+ ux + sx2 +tx3NOTE: 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 tto 4 decimal places.The weekly profit model has roots at x =-52.789, a 47.555, and x = 202.944, rounded to 3decimal places.The marginal weekly profit model has roots at a = -8.488 and a 140.295, rounded to 3decimal places.What is the maximum weekly profit? Round to the nearest dollar.24What is the wholesale price per sleeping bag that should be charged to realize the maximum weeklyprofit? Round to the nearest cent.per sleeping bagLo* Accessibility: Investigateere to searçch

Given, x is sleeping bags p is price and c is cost

Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: • p is 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.

Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: • p is 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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

What is the maximum weekly profit? What is the wholesale price per sleeping bag that should be charged to realize the maximum weekly profit?

Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the
price-demand and total cost data, where:
• p is the wholesale price (in dollars) of a sleeping bag for a weekly demand of r sleeping bags;
. Cis the total cost (in dollars) of producing r sleeping bags.
a(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 + bx + cz
Round a to the nearest intege
round b to 2 decimal places, and round e to 4 decimal places.
Revenue Model
Using the regression model computed above, find a model for the weekly revenue, using a as the
independent variable.
NOTE: Do not calculate another regression. Use the price equation to find a model for revenue
R(z) = p.r.
R(z) = p.r=(a+ bz + cx?)r ax + bx? + cz³
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
nere to search
N

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 x =-52.789, a 47.555, and x = 202.944, rounded to 3
decimal places.
The marginal weekly profit model has roots at a = -8.488 and a 140.295, rounded to 3
decimal places.
What is the maximum weekly profit? Round to the nearest dollar.
24
What is the wholesale price per sleeping bag that should be charged to realize the maximum weekly
profit? Round to the nearest cent.
per sleeping bag
Lo
* Accessibility: Investigate
ere to searçch

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