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 will make the total cost of voyage of 1000 nautical miles a minimum?

     1. *answer of speed should be in nautical miles per hour*
     2. *1 ton of coal = 10 shillings    ( if anyone takes the pain to solve the Bonus)*

Bonus: What will be that minimum cost if voyage?


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