Weronika Malińska
BUSINESS MANAGEMENT
Exercise 20/164
PRODUCTION At a certain factory, the daily output is Q(L) = 60,000L1/3 units, where L denotes the size
of the labor force measured in worker-hours. Currently 1,000 worker-hours of labor are used each
day. Estimate the effect on output that will be produced if the labor force is cut to 940 worker-hours.
1
𝑄(𝐿) = 60000𝐿3
Q – daily output
L – worker-hours
X0 = 1000
1000  940
Δx = -60
Δf ≈ f′(𝑥0 )Δx
−2
𝑄 ′ (𝐿) = 20000 ∗ 𝐿 3
ΔQ ≈ Q′ (1000) ∗ (−60) = 20000 ∗
1
3
2
(√1000)
∗ (−60) = 20000 ∗
1
∗ (−60) = −12000
100
Answer: If the labor force is cut to 940 worker-hours, the daily output will be lowered by about
12000 units.