Suppose that the number of crates of an agricultural product is given by 0.03x 2

Question

Suppose that the number of crates of an agricultural product is given by 0.03x 2y where x is the number of hours of labor and y is the number of acres of the crop Find the marginal productivity of the number of hours of labor (x) whenx 400 and y - 700. (Round your answer to two decimal places.) crates Interpret your answer. If 400 acres are planted, the expected change in the productivity for the 701st hour of labor is this many crates. O If 700 acres are planted and 400 hours are worked, this is the number of crates produced O If 400 acres are planted and 700 hours are worked, this is the number of crates produced. O If 700 acres are planted, the expected change in the productivity for the 401st hour of labor is this many crates

Explanation / Answer

Marginal productivity of no. of hours of labour = No. of creates produced with 401 labour - No. of creates produced with 400 labour

No. of crates (z) = (11xy - 0.0002x2 - 5y) / 0.03x+2y
Marginal productivity =
(11*401*700 - 0.0002*(401)2 - 5*700) / 0.03*401 + 2*700 - (11*400*700 - 0.0002*(400)2 - 5*700) / 0.03*400 + 2*700
=(3087700-32.16-3500)/1412.03 - (3080000-32-3500)/1412 = 2184 - 2179 = 5 units.

Thus marginal productivity of 401st labour hour is 5 crates.

Marginal productivity shows that
If 700 acres are planted, the expected change in the productivity for the 401st hour of labour is this many crates.

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