A company's production cost $P(n)$, in dollars, for producing $n$ widgets is modeled by a linear function $P(n)=mn+1000$, where $m$ is a constant representing the cost per widget and $1000$ is the fixed cost. If the total cost to produce 200 widgets is $1600, what is the total cost, in dollars, to produce 500 widgets? (Disregard the $ sign when gridding your answer.)