If I know the demand function of a new product is q(p)=10 - the square root of p, and I know that the cost function is C(x)=2x+45, how do I find the unit price that maximizes profit? What is the maximum profit? And how many items are sold at the optimizing price?
Not quite sure how p,q,x are related, but profit = revenue - cost
and revenue r = price * quantity
So, if you can sort those out, find where dr/dp = 0 and find q at that price p