A sports company has the following production function for a certain product, where p is the number of units produced with x units of labor and y units of capital. Complete parts (a) through (d) below. 4 1 p(x.y) = 2300x° y (a) Find the number of units produced with 26 units of labor and 1441 units of capital. p=O units (Round to the nearest whole number.) (b) Find the marginal productivities. "Py -0 dy (c) Evaluate the marginal productivities at x = 26 and y = 1441. P,(26,1441) =O (Round to the nearest whole number as needed.) P(26,1441) = (Round to the nearest whole number as needed.) (d) Interpret the meanings of the marginal productivities from part (c). O A. Supposing that capital fixed 1441 units, then a one-unit change in labor will cause production to increase by about 4107 units. Supposing that labor is fixed at 26 units, then a one-unit change in capital will cause production to increase by about 19 units. O B. Supposing that labor is fixed at 4107 units, then a one-unit change in capital will cause production to increase by about 1441 units. Supposing that capital is fixed at 19 units, then a one-unit change in labor will cause production to increase by about 26 units. OC. Supposing that labor is fixed increase by about 26 units. 4107 units, then a one-unit change in labor will cause production to increase by about 1441 units. Supposing that labor is fixed at 19 units, then a one-unit change in capital will cause production to O D. Supposing that labor is fixed 1441 units, then a one-unit change in capital will cause production to increase by about 4107 units. Supposing that capital is fixed at 26 units, then a one-unit change in labor will cause production to
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
A sports company has the following production function for a certain product, where p is the number of units produced with x units of labor and y units of capital. Complete parts (a) through (d) below.
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