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A factory produces baskets at a rate Q = x¹/3y¹/621/6 which it sells for p per item. The inputs x, y and z are positive quantities. The cost of production is C = w₁x + w₂y + w3z pounds with constants w₁, W2, w3. Find the critical values of x, y and z that make the profit a stationary value, and the value of the profit at this stationary value. First perform a general analysis and only at the end use the values w₁ 4, w34 and p = 8 x 6 = 48 to find values for the critical points and the value of the profit at these points. By computing the Hessian matrix at the critical point show also that this stationary value is a maximum. 8, W2 = =

A factory produces baskets at a rate Q = x¹/3y¹/621/6 which it sells for p per item. The inputs x, y and z are positive quantities. The cost of production is C = w₁x + w₂y + w3z pounds with constants w₁, W2, w3. Find the critical values of x, y and z that make the profit a stationary value, and the value of the profit at this stationary value. First perform a general analysis and only at the end use the values w₁ 4, w34 and p = 8 x 6 = 48 to find values for the critical points and the value of the profit at these points. By computing the Hessian matrix at the critical point show also that this stationary value is a maximum. 8, W2 = =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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A factory produces baskets at a rate Q = x¹/3y1/621/6 which it sells for p per item. The inputs x,y and z are positive quantities. The cost of production is C w₁x + w₂y + w3z pounds with constants w₁, W2, w3. Find the critical values of x, y and z that make the profit a stationary value, and the value of the profit at this stationary value. First perform a general analysis and only at the end use the values w₁ = 8, W2 = 4, w34 and p = 8 x 6 = 48 to find values for the critical points and the value of the profit at these points. By computing the Hessian matrix at the critical point show also that this stationary value is a maximum.
Transcribed Image Text:A factory produces baskets at a rate Q = x¹/3y1/621/6 which it sells for p per item. The inputs x,y and z are positive quantities. The cost of production is C w₁x + w₂y + w3z pounds with constants w₁, W2, w3. Find the critical values of x, y and z that make the profit a stationary value, and the value of the profit at this stationary value. First perform a general analysis and only at the end use the values w₁ = 8, W2 = 4, w34 and p = 8 x 6 = 48 to find values for the critical points and the value of the profit at these points. By computing the Hessian matrix at the critical point show also that this stationary value is a maximum.
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