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Home » Thus, the smallest such number is $\boxed120$. - AssociationVoting

Thus, the smallest such number is $\boxed120$. - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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y = 24 → as above → $1440
Best: x = 40, y = 0 → $1600
But try y = 15 → 5×15 = 75 → 3x ≤ 45 → x = 15 → P = 600 + 900 = $1500
Try y = 19 → 95 → 3x ≤ 25 → x = 8 → P = 320 + 1140 = $1460
Maximum occurs at x = 40, y = 0: $1600
However, check fractional optimization using slope method:
Slope of constraint: -3/5 = -0.6, profit slope = -40/-60 = 2/3 ≈ 0.67
Since 0.67 > 0.6, optimal not at intersection — check endpoints.
Thus, maximum profit is at x = 40, y = 0 → $1600
A science communicator creates a video explaining exponential growth u...

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