The Carlisle Innovation Company has created a new product that costs $25 per item to produce. The company has hired a marketing analyst to help it determine a selling price for the product. After collecting and analyzing data relating selling price s to yearly consumer demand d, the analyst estimates demand for the product using the equation
d = -200s + 15,000.
a. If yearly profit is the difference between total revenue and production costs, determine a selling price s, s ≥ 25, that will maximize the company's yearly profit, P
b. What are the risks of determining a selling price using this method?