# mathematical modeling and operational research

I have a variable TE which 0=<TE<=180

Also, I have a parameters L(k) and U(K), showing lower bound and upper bound for interval K (k=1,2,3)

The value of these parameters are as follows: L(1)=0 K(1)=60 , L(2)=60 K(2)=120, L(3)=120 K(3)=180

I need to find the related range of the variable TE. For example,

  if TE=12,  then K=1

if TE=150, then k=3


Which mathematical constraint(s) do this?

$$BOX(TE, L, U) = (TE > L)\; \& \;(TE < U)$$
$$k(TE) = 1 \cdot BOX(TE, L1, U1) + 2 \cdot BOX(TE, L2, U2) + 3 \cdot BOX(TE, L3, U3)$$