Now suppose the firm faces three types of consumers: Type A, Type B, and Type C with 100 consumers of each type. And the firm will produce high quality, medium quality, or low quality versions of the product. The marginal cost to produce the low quality version is $3 and the marginal cost to produce the medium quality version is $5 and the marginal cost to produce the high quality version is $15. Each consumer will buy at most one version of the product. These consumers have the following willingness to pay:

	Low Quality	Medium Quality	High Quality
Customer Type A	$14	$16	$28
Customer Type B	$16	$20	$33
Customer Type C	$18	$23	$52

Your task is to find the profit-maximizing prices for the high, medium, and low quality versions of the product assuming each consumer faces all prices and will purchase at most one version of the good. Find those three prices and the resulting profit!