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. 32 5 5 p(x,y)=2500x y (a) Find the number of units produced with 25 units of labor and 1064 units of capital. p= units (Round to the nearest whole number.) (b) Find the marginal productivities. ap ax ap =Px = = Py ду (c) Evaluate the marginal productivities at x = 25 and y=1064. Px (25,1064)= (Round to the nearest whole number as needed.). Py(25,1064)= (Round to the nearest whole number as needed.)

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.
3 2
5 5
p(x,y) = 2500xy
(a) Find the number of units produced with 25 units of labor and 1064 units of capital.
p= units
(Round to the nearest whole number.)
(b) Find the marginal productivities.
ap
dx
= Px
ap
ay
(c) Evaluate the marginal productivities at x = 25 and y = 1064.
Px (25,1064)=
(Round to the nearest whole number as needed.)
py (25,1064) =
(Round to the nearest whole number as needed.)
(d) Interpret the meanings of the marginal productivities from part (c).
O A. Supposing that labor is fixed at 6725 units, then a one-unit change in labor will cause production to increase by about 1064 units. Supposing that labor is fixed at 105 units, then a one-unit
change in capital will cause production to increase by about 25 units.
= Py
B. Supposing that labor is fixed at 1064 units, then a one-unit change in capital will cause production to increase by about 6725 units. Supposing that capital is fixed at 25 units, then a one-unit
change in labor will cause production to increase by about 105 units.
OC. Supposing that capital is fixed at 1064 units, then a one-unit change in labor will cause production to increase by about 6725 units. Supposing that labor is fixed at 25 units, then a one-unit
change in capital will cause production to increase by about 105 units.
O D. Supposing that labor is fixed at 6725 units, then a one-unit change in capital will cause production to increase by about 1064 units. Supposing that capital is fixed at 105 units, then a one-unit
Transcribed Image Text: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. 3 2 5 5 p(x,y) = 2500xy (a) Find the number of units produced with 25 units of labor and 1064 units of capital. p= units (Round to the nearest whole number.) (b) Find the marginal productivities. ap dx = Px ap ay (c) Evaluate the marginal productivities at x = 25 and y = 1064. Px (25,1064)= (Round to the nearest whole number as needed.) py (25,1064) = (Round to the nearest whole number as needed.) (d) Interpret the meanings of the marginal productivities from part (c). O A. Supposing that labor is fixed at 6725 units, then a one-unit change in labor will cause production to increase by about 1064 units. Supposing that labor is fixed at 105 units, then a one-unit change in capital will cause production to increase by about 25 units. = Py B. Supposing that labor is fixed at 1064 units, then a one-unit change in capital will cause production to increase by about 6725 units. Supposing that capital is fixed at 25 units, then a one-unit change in labor will cause production to increase by about 105 units. OC. Supposing that capital is fixed at 1064 units, then a one-unit change in labor will cause production to increase by about 6725 units. Supposing that labor is fixed at 25 units, then a one-unit change in capital will cause production to increase by about 105 units. O D. Supposing that labor is fixed at 6725 units, then a one-unit change in capital will cause production to increase by about 1064 units. Supposing that capital is fixed at 105 units, then a one-unit
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