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
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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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