Question 2: Consider 4 sets as follows: W = {w_1, w_2, w_3}, X = {x_1…

Consider 4 sets as follows: $W = \{w_1, w_2, w_3\}$, $X = \{x_1, x_2\}$, $Y = \{y_1, y_2, y_3\}$ and $Z = \{z_1, z_2\}$.

Given capacity constraints are as follows:

$c(w_2) = c(y_1) = c(y_3) = 1,$

$c(w_1) = c(w_3) = c(x_2) = c(y_2) = c(z_1) = 2,$

$c(x_1) = c(z_2) = 3$

$c(w_i, x_i) = 1, \text{ for all } w_i \in W \text{ and all } x_i \in X,$

$c(y_i, z_i) = 1, \text{ for all } y_i \in Y \text{ and all } z_i \in Z$

$c(x_1, y_1) = 1, c(x_1, y_2) = 2, c(x_1, y_3) = 1$

$c(x_2, y_1) = 0, c(x_2, y_2) = 2, c(x_2, y_3) = 1.$

Identify the size of a largest collection of 4-tuples from the sets $W, X, Y$ and $Z$ satisfying the given constraints