question archive A farmer can produce f(x,y)=250sqrt(4x^2+y^2) units of produce by utilizing x units of labor and y units of capital

A farmer can produce f(x,y)=250sqrt(4x^2+y^2) units of produce by utilizing x units of labor and y units of capital

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A farmer can produce f(x,y)=250sqrt(4x^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=7.

?(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 7 units.

?(c)

Use part? (b) to estimate the change in production when labor decreases from 12 to 10.5 units and capital stays fixed at 7 units.

?(a) The marginal productivity of labor when x=12 and y=7 is _________.

?(Simplify your? answer.)

The marginal productivity of capital when x=12 and y=7 is ___________.

?(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 7 units.

Production will change approximately ________ units.

?(c) Use part? (b) to estimate the change in production when labor decreases from 12 to 10.5 units and capital stays fixed at 7 units.

The production will decrease approximately ________ units.

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