A hospital performs $3$ types of operations. The first type takes $30$ minutes, and they charge $$1000$ for it$.$ The second type takes $1$ hour, and they charge $$1500$ for it$.$ The third operation takes $2$ hours, and they charge $$2000$ for it$.$ The hospital can schedule up to $20$ total operations per day. Moreover, they have $2$ operating rooms, each of which can be used for $8$ hours per day. Determine how many of each type of operation the hospital would perform to maximize its revenu