Lagrange multipliers - isothermal-isobaric ensemble

I know that the entropy of isothermal-isobaric ensemble is given by:

$$S = -k sum_{i=1}^M p_i ln p_i quad textrm{where $p_i$ must be normalized} quad sum_{i=1}^M p_i = 1 , .$$

The average energy is

$$sum_{i=1}^M p_i varepsilon_i = langle E rangle$$

and the average volume is

$$sum_{i=1}^M p_i V_i = langle V rangle , .$$

Some authors say that the probability of finding and state $i$ is given by

$$p_i = frac{1}{Q} , exp (-beta varepsilon_i – gamma V_i)$$

where $beta$ and $varepsilon$ are Lagrange multipliers.

I need to physically interpret these two terms. I compared

$$S = k , ln , Y + k beta langle E rangle + k gamma langle V rangle$$

with

$$S = – frac{G}{T} + frac{langle E rangle}{T} + frac{P langle V rangle}{T}$$

Where I can obtain that

$$G = -kT , ln Y, quad gamma = frac{P}{kT} quad textrm{and} quad beta = frac{1}{kT} , .$$

How can I obtain this equation using Lagrange?

$$p_i = frac{1}{Q} , exp (-beta varepsilon_i – gamma V_i)$$

I need some idea to open this equation, given that the physical interpretation of this parameters were done.