Answer
He needs to sell $1500$ cans of soda pop to gain a maximum profit of $450$ dollars.
Work Step by Step
$P(x)=-0.001x^2+3x-1800$
The maximum value of the function occurs at:
$x=\frac{-b}{2a}=\frac{-3}{-0.002}=1500$
Therefore, our maximum profit is:
$P(1500)=-0.001*1500^2+3*1500-1800=-0.001*2250000+4500-1800=-2250+2700=450$
In conclusion, his maximum profit is $450$ dollars when he sells $1500$ cans of soda pop.
