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The table contains price-demand and total cost data for the production of extreme-cold sleeping bags, where p is the wholesale price (in dollars) of a sleeping bag for an annual demand of x sleeping bags and C is the total cost (in dollars) of producing x sleeping bags. Complete parts (A) through (C) below. 960 230 1,150 1,900 2,100 210 165 120 (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. p(x) = Ox? + (Dx+ (O (Round the constant to four decimal places as needed. Round other values to six decimal places as needed) (B) Find a linear regression equation for the cost data, using x as the independent variable. C(x) = Ox+O (Round to three decimal places as needed.)

The table contains price-demand and total cost data for the production of extreme-cold sleeping bags, where p is the wholesale price (in dollars) of a sleeping bag for an annual demand of x sleeping bags and C is the total cost (in dollars) of producing x sleeping bags. Complete parts (A) through (C) below. 960 230 1,150 1,900 2,100 210 165 120 (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. p(x) = Ox? + (Dx+ (O (Round the constant to four decimal places as needed. Round other values to six decimal places as needed) (B) Find a linear regression equation for the cost data, using x as the independent variable. C(x) = Ox+O (Round to three decimal places as needed.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 67E
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The table contains price-demand and total cost data for the production of extreme-cold sleeping bags, where p is the wholesale price (in dollars) of a sleeping bag for an annual demand of x sleeping bags and C is the total cost (in dollars) of producing x sleeping bags. Complete parts (A) through (C) below. 960 230 1,150 1,900 2,100 130,000 150,000 180,000 200,000 210 165 120 (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. p(x) = (x2 + (*+ (D (Round the constant to four decimal places as needed. Round all other values to six decimal places as needed) (B) Find a linear regression equation for the cost data, using x as the independent variable. C(X) = Ox+ O (Round to three decimal places as needed.) (C) What is the form of the equation for profit? Write the profit function in terms of the variables from the table, x, p, and C. profit = What is the maximum profit? The maximum profit is $ (Round to the nearest dollar as needed.) What is the wholesale price per extreme-cold sleeping bag that should be charged to realize the maximum profit? The wholesale price per extreme-cold sleeping bag that should be charged to realize the maximum profit is $ (Round to the nearest dollar as needed.)
Transcribed Image Text:The table contains price-demand and total cost data for the production of extreme-cold sleeping bags, where p is the wholesale price (in dollars) of a sleeping bag for an annual demand of x sleeping bags and C is the total cost (in dollars) of producing x sleeping bags. Complete parts (A) through (C) below. 960 230 1,150 1,900 2,100 130,000 150,000 180,000 200,000 210 165 120 (A) Find a quadratic regression equation for the price-demand data, using x as the independent variable. p(x) = (x2 + (*+ (D (Round the constant to four decimal places as needed. Round all other values to six decimal places as needed) (B) Find a linear regression equation for the cost data, using x as the independent variable. C(X) = Ox+ O (Round to three decimal places as needed.) (C) What is the form of the equation for profit? Write the profit function in terms of the variables from the table, x, p, and C. profit = What is the maximum profit? The maximum profit is $ (Round to the nearest dollar as needed.) What is the wholesale price per extreme-cold sleeping bag that should be charged to realize the maximum profit? The wholesale price per extreme-cold sleeping bag that should be charged to realize the maximum profit is $ (Round to the nearest dollar as needed.)
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