Step by step explanations with correct mathematics explanation

Imagine that the supply and demand curves in the market for New York City hotel rooms given by Ps = 270 + Q/10 and PD = 300 - Q/5 (where P is measured in dollars per night and Q is measured in thousands of rooms per night). Suppose the NYC government levies a tax of $12 per room per night, collected from buyers. Evaluate the following statements: i. Before the tax, the sellers' revenue is more than $10 billion per year. li. After the tax, the sellers' revenue is less than $10 billion per year. ili. The government collects more than $500 million per year in revenue. iv. The fraction of the tax which the buyer bears is 2/3. Answers follow the order above. O true, true, true, true O true, true, true, false O true, true, false, true O true, true, false, false O true, false, true, true O true, false, true, false O true, false, false, true O true, false, false, false O false, true, true, true O false, true, true, false false, true, false, true O false, true, false, false O false, false, true, true O false, false, true, false