The cost function is total costs for the units produced. Don't multiply by the units.
Profit = revenues - costs
= (units*price) - costs
= x(1600-4x) - (40x+2000).
However, when I maximize this I still don't arrive at the answer given. I get x = 1560/8 = 195, p = 1600-4x = 820, not 824. Profits are different, too.