Cobb-Douglas Production Function A manufacturer estimates that its production can be modeled by f ( x , y ) = 100 0.8 y 0.2 where x is the number of units of labor and y is the number of units of capital. (a) Find the production level when x = 100 and y = 200. (b) Find the production level when x = 500 and y = 1500.
Cobb-Douglas Production Function A manufacturer estimates that its production can be modeled by f ( x , y ) = 100 0.8 y 0.2 where x is the number of units of labor and y is the number of units of capital. (a) Find the production level when x = 100 and y = 200. (b) Find the production level when x = 500 and y = 1500.
Solution Summary: The author explains that the given equation is f(x,y)=100x.8y
(4) (10 points) Evaluate
√(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV
where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z.
Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸
(2) (12 points) Let f(x,y) = x²e¯.
(a) (4 points) Calculate Vf.
(b) (4 points) Given x
directional derivative
0, find the line of vectors u =
D₁f(x, y) = 0.
(u1, 2) such that the
-
(c) (4 points) Let u= (1+3√3). Show that
Duƒ(1, 0) = ¦|▼ƒ(1,0)| .
What is the angle between Vf(1,0) and the vector u? Explain.
Find the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.)
a
b
29
39
66.50
C
17.40
d
0
54.0
126°
a
Ꮎ
b
d
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