Split of fuel oil consumption to heatup multiple type liquid

[sandeepbwes]

I have three different liquids l1, l2 and l3 stored for 10 days. The liquid are required to be kept in temp x1, x2 and x3.

As input i have following:
1) daily temp of all three liquids
2) daily qty
i need to keep temp of all three liquid constant - to do that heating is done. Due to heating fuel is consumed i keep track of daily consumed fuel.
Now my question is - how can the total daily consumed fuel be split so that i can know how much fuel is spent on l1, l2 and l3.
restrictions:
i cannot change (they are recorded and is to be treated as fixed):
1. Daily consumed fuel (total of all three liquids)
2. Daily individual temp of each liquid
3. Sum total of fuel consumed for 10 days.

Can anyone help me in guiding as to how should i proceed. The simple qty*variation in temp formula does not work (it allocates excessive fuel oil consumption in case where there has been drop in liquid temperature). Would really appreciate if someone out there can help me.

 

[Future Bruno]

Thanks.One possible way to approach this problem is to use linear programming to solve for the optimal fuel allocation. You can formulate the problem as an optimization problem where you minimize the total fuel consumed by allocating fuel to each liquid. Your constraints would include the total daily fuel consumed, daily individual temperature of each liquid, and the sum total of fuel consumed for 10 days. You can then use a linear programming solver to find the optimal fuel allocation that satisfies these constraints.