The only restraints on profit result from the restriction on the domain which in turn place a restriction on profit.
0≤k. Knives sold cannot be negative.
So the range of profit or p is:
p=[-500, +oo)
Profit increases as the number of knives sold increases. $200 more profit is gained by each sale of a knife.
4000=200k-500
4500=200k
k=22.5
Since k is for knives sold, it must be an integer value, so a $4000 profit is not possible. At 22, p=3900 and at 23, p=4100
