# Question #ef867

Apr 6, 2017

I am out of my turf here but you seem desperate so...I tried...

#### Explanation:

The Total Revenue Function should be:
$T R = P \cdot Q$
from the problem we have that $P = \frac{6000 - Q}{30}$
SO:
$T R = \frac{6000 - Q}{30} \cdot Q$
$T R = \frac{6000 Q - {Q}^{2}}{30}$

The Profit Function should be:
$P r = T R - T C$
$P r = \frac{6000 Q - {Q}^{2}}{30} - 5000 - 20 Q$
$P r = \frac{6000 Q - {Q}^{2} - 150000 - 600 Q}{30}$
$P r = \frac{5400 Q - {Q}^{2} - 150000}{30}$