This is a multilayered question. Could someone help me solve this problem and understand how the soultion was reached?

Suppose a plant produces a product that is highly differentiated. The product manager knows the production costs and the demand for the product. The daily cost function is estimated to be

TC = 500 - 15Q + 3Q²,

where Q refers to the daily volume of output and TC is the total cost. The demand for the product is

P= 153 - 4Q,

where P is the price and Q is the daily output and sales. The product manager wants to price the product and sell at a volume that maximizes profit.

i) To maximize profit, what volume of output per day should be produced?

ii) To maximize profit, what price should be set?

iii) How much profit will be made or loss incurred?