4. A firm can produce a quantity q(x, y) ((x + 1)³+y³)¹/3, in kg, of its good when it uses rkg of copper and ykg of iron. If copper and iron cost r and s pounds per kg respectively, use the method of Lagrange multipliers to find the bundle of copper and iron that will minimise this firm's costs if it has to produce Qkg of its good. [You are not required to justify the use of the method of Lagrange multipliers here.] Also find this firm's minimum cost, C(Q), and verify that C'(Q) is equal to the value of the Lagrange multiplier. In what ratio should this firm decrease the amount of copper and iron in their optimal bundle if they want to obtain the greatest decrease in their cost?
4. A firm can produce a quantity q(x, y) ((x + 1)³+y³)¹/3, in kg, of its good when it uses rkg of copper and ykg of iron. If copper and iron cost r and s pounds per kg respectively, use the method of Lagrange multipliers to find the bundle of copper and iron that will minimise this firm's costs if it has to produce Qkg of its good. [You are not required to justify the use of the method of Lagrange multipliers here.] Also find this firm's minimum cost, C(Q), and verify that C'(Q) is equal to the value of the Lagrange multiplier. In what ratio should this firm decrease the amount of copper and iron in their optimal bundle if they want to obtain the greatest decrease in their cost?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![4.
A firm can produce a quantity
q(x, y)
((x + 1)³+y³)¹/3,
in kg, of its good when it uses rkg of copper and ykg of iron.
If copper and iron cost r and s pounds per kg respectively, use the method of Lagrange
multipliers to find the bundle of copper and iron that will minimise this firm's costs if it
has to produce Qkg of its good.
[You are not required to justify the use of the method of Lagrange multipliers here.]
Also find this firm's minimum cost, C(Q), and verify that C'(Q) is equal to the value of
the Lagrange multiplier.
In what ratio should this firm decrease the amount of copper and iron in their optimal
bundle if they want to obtain the greatest decrease in their cost?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b719f4c-b890-4db8-ac16-88dcc60a450d%2Fe2a67b2e-685f-4f31-9e14-4c237c5cc1a8%2Fqp8wpnw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4.
A firm can produce a quantity
q(x, y)
((x + 1)³+y³)¹/3,
in kg, of its good when it uses rkg of copper and ykg of iron.
If copper and iron cost r and s pounds per kg respectively, use the method of Lagrange
multipliers to find the bundle of copper and iron that will minimise this firm's costs if it
has to produce Qkg of its good.
[You are not required to justify the use of the method of Lagrange multipliers here.]
Also find this firm's minimum cost, C(Q), and verify that C'(Q) is equal to the value of
the Lagrange multiplier.
In what ratio should this firm decrease the amount of copper and iron in their optimal
bundle if they want to obtain the greatest decrease in their cost?
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