Chapter summary
647
using x skilled and y anskilled workers, a manufacturer can produce q(x, y) = 60x^1/3y^2/3 units per day.
currently the manufacturer employs 10 skilled
workers and 40 unskilled workers and is planning
to hire 1 additional skilled worker. use calculus to
estimate the corresponding change that the
manufacturer should make in the level of unskilled
labor so that the total output will remain the
er summary
same.

The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.

Step-by-step explanation:

Q(x,y) = 60 x^⅓ y^⅔

Take the partial derivatives with respect to x and y.

∂Q/∂x = 20 x^-⅔ y^⅔

∂Q/∂y = 40 x^⅓ y^-⅓

So the total differential is:

dQ = ∂Q/∂x dx + ∂Q/∂y dy

dQ = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dy

If dQ = 0:

0 = 20 x^-⅔ y^⅔ dx + 40 x^⅓ y^-⅓ dy

If x = 10, y = 40, and dx = 1:

0 = 20 (10)^-⅔ (40)^⅔ (1) + 40 (10)^⅓ (40)^-⅓ dy

0 = 20 (4)^⅔ + 40 (1/4)^⅓ dy

-20 (4)^⅔ = 40 (1/4)^⅓ dy

-20 (4)^⅔ (1/4)^⅔ = 40 (1/4)^⅓ (1/4)^⅔ dy

-20 = 40 (1/4) dy

-20 = 10 dy

dy = -2

The manufacturer should decrease the level of unskilled labor by 2 for the total output to stay the same.

u bout ugly as   a mf

step-by-step explanation: lol

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic