The symmetric monoidal preorder \(\mathbf{Cost}:=([0,\infty],\geq,0,+)\) is monoidal closed.
For any \(x,y \in [0,\infty]\), define \(x \multimap y := max(0,y-x)\)
Then, for any \(a,x,y\), we have \(a+x\geq y\) iff \(a \geq y-x\) iff \(max(0,a)\geq max(0,y-x)\) iff \(a \geq (x \multimap y)\)
We can use this to define a notion of subtraction in Cost.