Yenter Outfers manactures and sels extreme-cold sleeping bap. The table below shows the pricedenndnd total cost data where Revenue Model phthe wholesale price n dolanofa seeping bag for a weekly demand of a sleeping bags Chthe total cost n dolars of producing a sleeping bags Using the regression model computed above, find a model for the weekly revenue, using z as the eeeping bap independent variable. 240 13.000 NOTE: Do not calculate another regression. Use the price equation to find a model for revenue R(2) -Pz. (120 225 4300 180 155 8.500 R(z) = p- z = (a + bz + cz*)z = az + br² + cz² 220 50 21000

Given information: Given data represents the values of the variables x = sleeping bags, p = price and c = cost.Find the cost model: EXCEL software can be used to plot a least squares line on a scatter diagram for the given data. Software Procedure: The step-by-step procedure to plot a least squares line on a scatter diagram using EXCEL software is given below: Open an EXCEL file. Enter the data of Sleeping bags in column A and name it as x. Enter the data of Cost in column B and name it as C. Select Data and go to Insert tab. Select Charts > All charts > Scatter (X Y). Click OK. Select any point on the Scatterplot and left click on it. Select add trendline > linear and click on display equation. The output is as shown below: The cost model is: C(x) = 65.2x + 6674.Find the price model: EXCEL software can be used to plot a least squares line on a scatter diagram for the given data. Software Procedure: The step-by-step procedure to plot a least squares line on a scatter diagram using EXCEL software is given below: Open an EXCEL file. Enter the data of Sleeping bags in column A and name it as x. Enter the data of Price in column B and name it as p. Select Data and go to Insert tab. Select Charts > All charts > Scatter (X Y). Click OK. Select any point on the Scatterplot and left click on it. Select add trendline > polynomial > order = 2 and click on display equation. The output is as shown below: The price model is: p = 112 + 2.59x – 0.0131x2Find the revenue model: The revenue model is as given below: R(x) = p*x = (112 + 2.59x – 0.0131x2)*x = 112x + 2.59x2 – 0.0131x3. Find the profit model: The profit model is: p(x) = R(x) – c(x) = 112x + 2.59x2 – 0.0131x3 – 65.2x – 6674 = 2.59x2 – 0.0131x3 + 46.8x – 6674 Find the maximum weekly profit: The maximum weekly profit is obtained as given below: p(x) = 2.59x2 – 0.0131x3 + 46.8x – 6674 p1(x) = 5.18x – 0.0393x2 + 46.8 = – 0.0393x2 + 5.18x + 46.8 p1(x) = 0 – 0.0393x2 + 5.18x + 46.8 = 0 0.0393x2 – 5.18x – 46.8 = 0 x = 140.295 and x = 8.48813 Maximum profit = 2.59*140.2952 – 0.0131*140.2953 + 46.8*140.295 – 6674 = 14696 Find the wholesale price: p = 112 + 2.59x – 0.0131x2 = 112 + 2.59*140.295 – 0.0131*140.2952 = 218

Answered: Yenter Outfers manactures and sels extreme-cold sleeping bap. The table below shows the pricedenndnd total cost data where Revenue Model phthe wholesale price n…

MATLAB: An Introduction with Applications

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Author: Amos Gilat

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

What is the wholesale price per sleeping bag that should be charged to realize the maximum weekly
profit? Round to the nearest cent.
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Yaster Outhtters manufactures and sells extreme-cold sleeping bags. The table below shows the
price-demand and total cost data, where:
Revenue Model
pis the wholesale price (in dollars) of a sleeping bag for a weekly demand of a sleeping bags:
.Cis the total cost (in dollars) of producing z sleeping bags.
Using the regression model computed above, find a model for the weekly revenue, using a as the
(sleeping bags)
P (S)
C ($)
independent variable.
95
240
13.000
NOTE: Do not calculate another regression. Use the price equation to find a model for revenue
120
235
14,300
R(x)= p aæ.
180
155
18,500
R(x) = p·x = (a + bx + cx²)x
= ax + bx²+ cr³
220
50
21.000
1
Cost Model
Find a linear regression model for the weekly cost data, using a as the independent variable.
C(x) = mx + k
Find a quadratic regression equation for the price-demand data, using x as the independent variable.
p= a+ bx + cx²
Round m to 1 decimal place, and round k to the nearest integer.
Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places.
Profit Model
Use the models computed to find a model for the weekly profit, using x as the independent variable.
The weekly profit model has roots at x = -52.789, x=
47.555, and x =
202.944, rounded to 3
P(z) =r+ux + sx² + tx³
decimal places.
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
The marginal weekly profit model has roots at x = -8.488 and x =
140.295, rounded to 3
to 4 decimal places.
decimal places.
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