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 = =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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