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Suppose a unit of capital costs $2 and a unit of labour costs $4. The production function is Q = 6KL + 2L². (a) Using Lagrange multipliers calculate the maximum possible output Q when the total input cost is $200. (b) Measuring labour (L) on X-axis and capital (K) on Y-axis, show the optimal level of L and K in a diagram.

Suppose a unit of capital costs $2 and a unit of labour costs $4. The production function is Q = 6KL + 2L². (a) Using Lagrange multipliers calculate the maximum possible output Q when the total input cost is $200. (b) Measuring labour (L) on X-axis and capital (K) on Y-axis, show the optimal level of L and K in a diagram.

Advanced Engineering Mathematics
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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Please explain how to get the equation when its equal to 200

Suppose a unit of capital costs $2 and a unit of labour costs $4. The production function is Q = 6KL + 2L². (a) Using Lagrange multipliers calculate the maximum possible output Q when the total input cost is $200. (b) Measuring labour (L) on X-axis and capital (K) on Y-axis, show the optimal level of L and K in a diagram.
Transcribed Image Text:Suppose a unit of capital costs $2 and a unit of labour costs $4. The production function is Q = 6KL + 2L². (a) Using Lagrange multipliers calculate the maximum possible output Q when the total input cost is $200. (b) Measuring labour (L) on X-axis and capital (K) on Y-axis, show the optimal level of L and K in a diagram.
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