Let there be two types of consumer, A and B. A has utility given by 12q p. B has utility

given by 5q p, where q is a numerical index of quality and p is the price of a unit. There are

three times as many Type B's as there are A's. The total number of consumers is 400. The marginal cost of serving each individual consumer's purchase is 4q. This means the total variable cost of serving a consumer is equal to 2q^2. The firm must also incur a fixed cost of production equal to F.

Given that the firm cannot distinguish a A from a B, would the firm want to operate if F = 1000?