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Algebra
Pregunta

A farmer can produce \( f ( x , y ) = 150 \sqrt { ...

A farmer can produce \( f ( x , y ) = 150 \sqrt { 4 x ^ { 2 } + y ^ { 2 } } \) units of produce by utilizing \( x \) units of labor and \( y \) units of capital.

 

 (a) Calculate the marginal productivities of labor and capital when \( x = 6 \) and \( y = 9 \) . 

 

(b) Let \( h \) be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from \( 6 \) to \( 6 \) + \( h \) units while keeping capital fixed at \( 9 \) units. 

 

(c) Use part (b) to estimate the change in production when labor decreases from \( 6 \) to \( 4.5 \) units and capital stays fixed at \( 9 \) units. 

 

(a) The marginal productivity of labor when \( x = 6 \) and \( y = 9 \) is \( \square \) . (Simplify your answer.) 

Answer

2250

Solución
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