Financial and optimization applications

Discrete math tools apply directly to resource and business decisions. A break-even analysis finds where total cost meets total revenue: if a product costs $200 to set up plus $3 per unit, and sells for $8 per unit, break-even happens when 200 + 3x = 8x, giving x = 40 units. Optimization under limited resources means systematically comparing options: with 10 hours of oven time, baking 10 cakes (1 hour each, $5 profit) earns $50, while baking 5 pies (2 hours each, $8 profit) earns only $40, so cakes are the better use of the same 10 hours.

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