# 1920 Calculus Horror

Calculus Level 4

The consumption of coal by the 1920's steamer Ayumo may be represented by the formula $y=0.3+0.001v^{3}$, where $y$ represents number of tons of coal burned per hour and $v$ represents speed in nautical miles per hour.

Other costs of maintenance of ship and wages, per hour, is same as cost 1 ton of coal.

What speed (in nautical mules per hour) will minimize the total cost of a voyage of 1000 nautical miles?

Bonus: What will be that minimum cost of voyage if 1 ton of coal = 10 shillings

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