Suppose that the number of crates of an agricultural product is given by , where x is the number of hours of and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor when and .

Question

Suppose that the number of crates of an agricultural product is given by  , where x is the number of hours of and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor when  and  . ​

Quizplus · Accepted Answer

To find the marginal productivity of labor, we need to take the partial derivative of the production function with respect to labor, which in this case is the variable x.

∂Q/∂x = 11e^(9y-49x) * (-49)

Substituting x = 80 and y = 5, we get:

∂Q/∂x = 11e^(9(5)-49(80)) * (-49) = 25.39

Therefore, the marginal productivity of labor is 25.39 crates per hour when the number of hours is 80 and the number of acres is 5.

Suppose That the Number of Crates of an Agricultural Product