I want to solve the problem like this:-

The monopolist requires a profit(P) of at least 1500.

So, \(\displaystyle P \ge1500\)

or\(\displaystyle -10q^2+300q-500 \ge1500\)

or \(\displaystyle 10\le q\le20\)

So the monopolist must produce his output in the range of 10 to 20 units.It's given that the monopolist maximizes his revenue. So we have to find at what value of q, revenue is maximum.

At x=10, Revenue(R)= 304q-2q^2 = 2840

At x=20, Revenue(R)=5280

Clearly, as the monopolist goes on increasing his output from 10 units to 20 units, its revenue goes on increasing and becomes maximum at 20 units i.e., at x=20. So we conclude that the output level for the monopolist is x=20.

Here I've combined the suggestions of you two.

Please tell me if I'm right or wrong.