How much of the public good will be produced

Question

Question 1: Each of three programmers has utility for their oviit time X. and for the public good that comes from a joint effort G = g₁ + g₂ + g₃:

Utilify_i(X_i,G) = X^3/4_i * G^1/4, and T_i = X_i + g_i.

The programmers have total time of T1 = 16, T2 = 16, and T3 = 21, respectively.

Solving this problem either numerically or symbolically, how much of the public good will be produced and by whom?

Question 2: Do you think this arrangement is fair, and could you use the Yootles system to improve things?