Answer to Question #205382 in Calculus for Akhona Klanisi

Question

15

A firm’s production function is given by

Q = 700Le^−0,02L,

where Q denotes the number of units produced and L the number of labourers. Determine the size of the  workforce that maximises output.

[a.   L = 14

[b.   L = 50

[c.   L = 328

[d.   L = 700

Answer 1

Given,

$$Q=700Le^{-0.02L}$$

So, for maximize Q , we have to get value of L such that $Q'=0$

Here, $Q=700Le^{-0.02L}$

$\implies Q'=700[e^{-0.02L}+L(-0.02e^{-0.02L})]\\\implies Q'=700e^{-0.02L}-14Le^{-0.02L}$

$\implies Q'=(700-14L)e^{-0.02L}$

Let Q' = 0

So, $(700-14L)=0$

$\implies L=50$

Hence, the value of L is equal to 50 for maximum output

Option (b) is correct