Question

At a certain factory, the daily output is Q(L)= 42000L^(1/3), where L denotes the size of labor force measured in worker-hours. Currently, 1500 worker-hours of labor are used each day. Estimate the effect on output that will be produced if the labor force is
(A) cut to 1450 worker-hours
(B) increased to 1550 worker-hours

Answer 1

was the last answer correct? 27

Answer 2

yes it was

Answer 3

awesome :)

Answer 4

i think when it says 'estimate' we should use differentials

Answer 5

so how do we do that

Answer 6

dQ = dQ/dL * dL

Answer 7

i still don't understand

Answer 8

the idea is

Answer 9

dy = f'(x) * dx

Answer 10

we use dy to approximate the 'actual' change in y

Answer 11

so we use the derivative of the equation and we dx the equation ?

Answer 12

correct

Answer 13

I found an expression for dQ/dL, then i multiplied both sides by dL

Answer 14

and then for b you would just plug in 1550

Answer 15

Shouldn't dL be -50 for a) and +50 for b) ?

Answer 16

A) dQ = 42000 * 1/3 (1500)^(-2/3) * (-50)
B) dQ = 42000 * 1/3 (1500)^(-2/3) * (50)

Answer 17

why is -50

Answer 18

to go from the 'current' 1500 work hours to 1450 , thats -50

Answer 19

oh

Answer 20

dL is the 'increment' in L

Answer 21

im not sure what the units are for output, though

Answer 22

A) dQ = 42000 * 1/3 (1500)^(-2/3) * (-50) = -5341.999

B) dQ = 42000 * 1/3 (1500)^(-2/3) * (50)=5341.999

Answer 23

so the answers would be -5320 and 2128

Answer 24

I got , rounded to the nearest hundredth or tenth
-5342 , 5342

Answer 25

Aum saved my butt there

Answer 26

yes your right

Answer 27

np.