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+0.001v3y=0.3+0.001v^{3}, where yy represents number of tons of coal burned per hour and vv 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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