Consider the following details for a manufacturing company producing two products, Epsilon and Zeta:

24. 
    
    • Product Epsilon: Selling price $120, variable cost $65, fixed cost $30
    • Product Zeta: Selling price $180, variable cost $95, fixed cost $50

Determine the optimal production quantity for each product to maximize profit, given that the company can sell up to 3,000 units of each product and has a maximum of $70,000 in fixed costs. Provide a comprehensive explanation of your analysis.