Consider the following details for a manufacturing company producing two products, Theta and Iota:

30. 
    
    • Product Theta: Selling price $140, variable cost $75, fixed cost $35
    • Product Iota: Selling price $210, variable cost $110, fixed cost $55

Determine the optimal production quantity for each product to maximize profit, given that the company can sell up to 3,500 units of each product and has a maximum of $80,000 in fixed costs. Provide a comprehensive explanation of your analysis.