The production Q of a certain good in terms of the amount of labour invested L and the amount of capital invested K, is given by the production function Q = 5 L²/3 K ¹/3 At this moment 512 units of labour and 1 000 units of capital are invested daily. This means that at this moment 3200 units are produced daily. a) The company receives an order for 3200 units. Give an implicit equation for the combinations (L,K) resulting in a production of 3200 units. b) Determine K'(L) for L = 100 using implicit differentiation. Interpret your result in a sentence in the context of the word problem. c) Determine the following expression and interpret your result in a sentence in the context of the word problem: 100 K'(100) K d) Set up the graph of K as a function of L using a logarithmic scale on both axes. Interpret the slope in L = 100.

The production Q of a certain good in terms of the amount of labour invested L and the amount of capital invested K, is given by the production function Q = 5 L²/3 K ¹/3 At this moment 512 units of labour and 1 000 units of capital are invested daily. This means that at this moment 3200 units are produced daily. a) The company receives an order for 3200 units. Give an implicit equation for the combinations (L,K) resulting in a production of 3200 units. b) Determine K'(L) for L = 100 using implicit differentiation. Interpret your result in a sentence in the context of the word problem. c) Determine the following expression and interpret your result in a sentence in the context of the word problem: 100 K'(100) K d) Set up the graph of K as a function of L using a logarithmic scale on both axes. Interpret the slope in L = 100.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

The production of a certain good in terms of the amount of labour invested L and the amount of capital
invested K, is given by the production function Q = 5 L²/3 K ¹/3
At this moment 512 units of labour and 1 000 units of capital are invested daily. This means that at this moment
3200 units are produced daily.
a) The company receives an order for 3200 units. Give an implicit equation for the combinations (L, K)
resulting in a production of 3200 units.
b) Determine K'(L) for L = 100 using implicit differentiation. Interpret your result in a sentence in the
context of the word problem.
c)
Determine the following expression and interpret your result in a sentence in the context of the word
problem:
100
K'(100)
K
d) Set up the graph of K as a function of L using a logarithmic scale on both axes. Interpret the slope in
L = 100.

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