1. **Problem Statement:** (a) Determine the price of a tray of eggs and a kilo of sugar. 2. **Formulating the problem:** Let $x$ be the price of a tray of eggs and $y$ be the price of a kilo of sugar. 3. **Mathematical constraints:** Since the problem does not provide explicit equations or inequalities, we cannot form constraints without additional data. 4. **Feasible region and optimization:** Without constraints or objective function, we cannot determine the feasible region or maximize profits. 5. **Summary:** The problem statement is incomplete for parts (a) and (b). Please provide the prices or relationships between prices and quantities to proceed. --- **Note:** The user message contains multiple problems but only the first problem is solved as per instructions.