the demand function for a pair of sneakers is p=8-(4)sqrt(x) and the cost to produce it is given by the function c(x)=500+15x. What should the price be set to in order to maximize profit

Answer 1

Note that price per unit=8-4sqrt(x)=p where x= units sold and cost per unit = 500+15x=c. Profit is therefore = P=(p-c)x or -15x²-450x-4x^1.5=P ... note that P is <0 for any x>0 thus the best profit is zero with zero units being manufactured nor sold