Formulating a Linear Program for use in a Solver
I'm a bit lost on how to formulate this as a linear programming problem, or even if it's possible.

I have a set of laps which make up a total time, and for each lap a certain amount of power is used.  I need to minimise total time with respect to the total energy used being less than a certain constant.
So I've got the following equations:

 1. sum(Ti) = Ttotal   //want to minimise sum(Ti)
 2. sum(Pi * Ei) < c   //c is a constant, and Pi is a double between 0 and 1000
 3. Ti = d/ Vi    //where d is a constant distance, and Vi is the velocity used for that lap
 4. Vi = f(Pi)     //where f is some function, and Pi is the power.

So just to explain incase this is unclear, the inputs are the power for the lap (with Pi being power for lap i).  From this the velocity for the lap is calculated (Vi), and from that the time for the lap is calculated (Ti).  The energy for each lap is then calulated (Ti * Pi), and the total energy for all the laps has to be less than a constant, and  am trying to minimise total time.

Equations 2 and 4 is where I'm a bit lost if I can even do these as a set of linear equations, and if so how.


Formulating a Linear Program for use in a Solver
===

I'm a bit lost on how to formulate this as a linear programming problem, or even if it's possible.

I have a set of laps which make up a total time, and for each lap a certain amount of power is used.  I need to minimise total time with respect to the total energy used being less than a certain constant.
So I've got the following equations:

 1. sum(Ti) = Ttotal   //want to minimise sum(Ti)
 2. sum(Pi * Ei) < c   //c is a constant, and Pi is a double between 0 and 1000
 3. Ti = d/ Vi    //where d is a constant distance, and Vi is the velocity used for that lap
 4. Vi = f(Pi)     //where f is some function, and Pi is the power.

So just to explain incase this is unclear, the inputs are the power for the lap (with Pi being power for lap i).  From this the velocity for the lap is calculated (Vi), and from that the time for the lap is calculated (Ti).  The energy for each lap is then calulated (Ti * Pi), and the total energy for all the laps has to be less than a constant, and  am trying to minimise total time.

Equations 2 and 4 is where I'm a bit lost if I can even do these as a set of linear equations, and if so how.

