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Algebra
Pregunta

A farmer can produce \( f ( x , y ) = 162 \sqrt { ...

A farmer can produce \( f ( x , y ) = 162 \sqrt { 5 x ^ { 2 } + y ^ { 2 } } \) units of produce by utilizing \( x \) units of labor and \( y \) units of capital. (a) Calculate the marginal productivities of labor and capital when \( x = 12 \) and \( y = 3 \) . (b) Let \( h \) be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from \( 12 \) to \( 12 + h \) units while keeping capital fixed at \( 3 \) units. (c) Use part (b) to estimate the change in production when labor decreases from \( 12 \) to \( 11.5 \) units and capital stays fixed at \( 3 \) units. (a) The marginal productivity of labor when \( x = 12 \) and \( y = 3 \) is \( 360 \) . (Simplify your answer.) The marginal productivity of capital when \( x = 12 \) and \( y = 3 \) is \( 18 \) . (Simplify your answer.) (b) Let \( h \) be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from \( 12 \) to \( 12 + h \) units while keeping capital fixed at \( 3 \) units. Production will change approximately \( \square \) units. 

Answer

360

Solución
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