Formulate the problem to maximize profit:
Our company sells two types of novelty items to local bookstores. Type 1 generates $3 profit for each unit sold and Type 2 generates $5 profit for each unit sold. Market conditions indicate that we cannot sell more than 4 units of Type 1 and more than 6 units of Type 2. We have 18 hours of labor available. Type 1 and Type 2 products require 3 hours and 2 hours of labor per unit respectively. Inventory policy dictates that we must deplete at least 50 units of raw material. Type 1 items require 3 units of raw material and Type 2 items require 5 units of raw material.