On a section of a highway the speed-density relationship

On a section of a highway the speed-density relationship is linear and is
given by v = 80 - 2 k ;
3

where v is in km/h and k is the veh/kem. The capacity (in veh/h) of this section of the highway would be

Given , V = 80 -	2	k
	3

Capacity of section, q = V × k

=		80 -	2	k		× k = 80k -	2	k² .......(1)
			3				3

For maximum q,
Differentiate q. wrt k

	dq	= 0
	dk

⇒ 80 -	4	k = 0
	3

⇒ k = 60
Substitute in (1)

q = 80 × 60 -	2	× 60² = 2400 veh / hr
	3

given by v =		80 -	2	k		;
			3