The Rainwater Brewery produces beer. The annual fixed cost is $150,000, and the variable cost per barrel

Question:

The Rainwater Brewery produces beer. The annual fixed cost is $150,000, and the variable cost per barrel is $16. Price is related to demand, according to the following linear equation:
v = 75,000 - 1,153.8p

Develop the nonlinear profit function for the brewery and determine the price that will maximize profit, the optimal volume, and the maximum profit per year.