Suppose the Sunglasses Hut Company has a profit function given by P(q)=−0.02q^2+3q−37,

Question

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

A) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.)

Answer: _____ thousand pairs of sunglasses need to be sold.

B) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.)

Answer: _____ thousand dollars of maximum profits can be expected.

Answer 1

The maximum will occur at the vertex. You can find the vertex manually using x coordinate = -b/2a

Once you find x, you can plug that in to find y.

I chose to use the TI-84 graphing calculator max feature to find the vertex.

a) 75 (x coordinate)

b) 75.5 (y coordinate)