How can I mathematically model the combinatory problem?

Question

I have the following problem, and I would like to model it using a mathematical formula, for a purpose of optimization problem:

let's say that I have two tasks $[T_1, T_2]$, and $3$ resources $[R_1,R_2,R_3]$, each resource has a price $P$.

I would like to find the formula which found the best combination of [task, resource], let's say the maximum combination of the following sums:

$Max$$[(T_1/P_1 + T_2/P_1), (T_1/P_1 + T_2/P_2), (T_1/P_1 + T_2/P_3), (T_1/P_2 + T_2/P_1), (T_1/P_2 + T_2/P_2), (T_1/P_2 + T_2/P_3), (T_1/P_3 + T_2/P_1), (T_1/P_3 + T_2/P_2), (T_1/P_3 + T_2/P_3)]$

Regards.

Answer 1

You have a classical assignment problem. The wiki entry should have enough info to get you started on modeling it.