Suppose the Sunglasses Hut Company has a profit function given by P(q)=0.03q2+5q45 where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses.

How many pairs of sunglasses (in thousands) should be sold to maximize profits?

What are the actual maximum profits (in thousands) that can be expected?