1. **State the problem:** Marie-Eve runs a daycare charging 12 per baby and 8 per toddler per day. A new law restricts the total number of children (babies + toddlers) to a maximum of 20. We want to find how much her maximum daily revenue decreases due to this new law. 2. **Define variables and constraints:** Let $b$ = number of babies, $t$ = number of toddlers. Revenue function: $$R = 12b + 8t$$ Original constraints (from polygon vertices): points (0,20), (10,10), (20,0) form a triangle. This implies the constraint line: $$b + t = 20$$ But original constraints allowed up to 30 children on each axis, so original max children could be up to 30 babies or 30 toddlers. 3. **Find original maximum revenue without new law:** The polygon vertices are (0,20), (10,10), (20,0). Check revenue at each vertex: - At (0,20): $$R = 12\times0 + 8\times20 = 160$$ - At (10,10): $$R = 12\times10 + 8\times10 = 120 + 80 = 200$$ - At (20,0): $$R = 12\times20 + 8\times0 = 240$$ Maximum revenue originally is $$240$$ at (20,0). 4. **Find maximum revenue with new law:** New law restricts total children to max 20, so $$b + t \leq 20$$. The polygon formed by (0,20), (10,10), (20,0) already respects this. But original constraints allowed up to 30 babies or toddlers individually, so original max revenue could be higher. Check revenue at (0,30): $$R = 12\times0 + 8\times30 = 240$$ Check revenue at (30,0): $$R = 12\times30 + 8\times0 = 360$$ Check revenue at (0,0): $$R=0$$ So original max revenue without the new law is $$360$$ at (30,0). 5. **Calculate revenue decrease:** Maximum revenue before new law: $$360$$ Maximum revenue after new law: $$240$$ Decrease in maximum revenue: $$360 - 240 = 120$$ 6. **Answer:** The maximum possible daily revenue decreases by **120** due to the new law.