I'm using the example of cargo on a ship to demonstrate one variable reliant on another and how to find the peak value of each variable that gets the most out of both.
So lets say you want to ship cargo from one country to another. You want to build the ship but you want to find out what is the most efficient cargo weight that provides the most efficient speed, meaning, would carrying 100 tons at 60mph work out better than 150 tons at 45mph?
Focusing solely on the relationship between maximum speed and cargo weight, how would you propose working out the most efficient cargo weight that also obtains the highest speed.
I thought about multiplying the cargo weight by the speed and using a points system?
I'm curious to know this forums outlook to a situation like this or perhaps if there are any implemented methods already.
Thank you in advance.
If you multiply the weight by the speed you get a number with units of ton-miles/hour. If you know how much total cargo there is to move and the distance to move it, you can multiply them and divide by the ship product to get a number with units of hours. This is the time it will take to move the cargo. If you want to minimize that, you want to be dividing by the largest number you can, so you want to maximize the product of weight on the ship and ship speed.
What you need to make use of this is the relationship between weight and speed for the ships you can build. You solve that for one in terms of the other and plug it into the weight-speed product, giving an expression in one variable. Take the derivative, set to zero.....