A small craftsman wants to plan the production of his star product: "the roguish man". The craftsman has realized through his years of experience that the demand for this product remains relatively constant at values close to 4 units per day. Suppose the craftsman is able to produce 12 rogue men per day. The craftsman may store his wares at a friend's house while waiting for them to be sold. This friend charges him $300 coins for each month that a roguish man stays in his house. The craftsman has a fixed production cost of $1,000 coins. Suppose finally that the manufacturing cost of each rogue man is $300 coins and that the sale price is $1500 coins.

1. Determine the optimal lot size by specifying and justifying the model used. 2. Calculate the total monthly cost of this productive policy. 3. Calculate the total monthly profits of this productive policy.