The student makes and sells necklaces at beach during summer months. Material for each necklace costs her $6 and she has been selling about 24 per day at $10 each. She has been thinking whether or not to raise price, so she takes the survey and discovers that for every dollar increase she would lose 2 sales a day.
(a) If she increases the price by x dollars, then price will be dollars, number of sales for the day will be necklaces, and her cost to make necklaces for day will be dollars.
(b) Write profit P as the function of number x of dollar increases in price:
(b) What price (to nearest cent) must she set for necklaces to maximize the profit?
(c) Determine maximum profit (to nearest cent)?