Consider the following details for a manufacturing company producing two products, Gamma and Delta:

18. 
    
    • Product Gamma: Selling price $100, variable cost $55, fixed cost $25
    • Product Delta: Selling price $150, variable cost $80, fixed cost $40

Determine the optimal production quantity for each product to maximize profit, given that the company can sell up to 2,500 units of each product and has a maximum of $60,000 in fixed costs. Provide a thorough explanation of your analysis.