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

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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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Transcribed Image Text:What is the wholesale price per sleeping bag that should be charged to realize the maximum weekly profit? Round to the nearest cent. O L C C 虱 F3 F4 F5 F6 F7 F8 PrtSc F9 F10 F11 F12 & T //Y F G K L %3B P * 00 44
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 ($)
independent variable.
95
240
13.000
NOTE: Do not calculate another regression. Use the price equation to find a model for revenue
120
235
14,300
R(x)= p aæ.
180
155
18,500
R(x) = p·x = (a + bx + cx²)x
= ax + bx²+ cr³
220
50
21.000
1
Cost Model
Find a linear regression model for the weekly cost data, using a as the independent variable.
C(x) = mx + k
Find a quadratic regression equation for the price-demand data, using x as the independent variable.
p= a+ bx + cx²
Round m to 1 decimal place, and round k to the nearest integer.
Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places.
Profit Model
Use the models computed to find a model for the weekly profit, using x as the independent variable.
The weekly profit model has roots at x = -52.789, x=
47.555, and x =
202.944, rounded to 3
P(z) =r+ux + sx² + tx³
decimal places.
NOTE: Do not calculate another regression. Use the fact that profit is revenue minus cost.
Round r to the nearest integer, round u to 1 decimal place, round s to 2 decimal places, and round t
The marginal weekly profit model has roots at x = -8.488 and x =
140.295, rounded to 3
to 4 decimal places.
decimal places.
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Transcribed Image Text:Yaster Outhtters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: Revenue Model pis the wholesale price (in dollars) of a sleeping bag for a weekly demand of a sleeping bags: .Cis the total cost (in dollars) of producing z sleeping bags. Using the regression model computed above, find a model for the weekly revenue, using a as the (sleeping bags) P (S) C ($) 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. I. rds Eo * Accessibility: Investigate O Focus 223% 1:42 AM LC W 77% pe here to search 11/17/2021 PrtSc Insert Delete F7 F8 F10 F11 F12 FS F5 F9 & Backspace 5 6 7. 80 %23
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