Question: A manufacturer has been selling lamps at $16 apiece, and at this price, consumers have been buying 5000 lamps per month. The manufacturer wishes to raise the price and estimates that for each $1 increase in the price 400 fewer lamps will be sold each month. The manufacturer can produce the lamps at a cost of $9 per lamp. At what price should the manufacturer sell the lamps to generate the greatest possible profit and what is the maximum profit that would be attained under these conditions?