Suppose a firm produces bowls and mugs from labor and clay. Let $x_1$ represent the number of bowls produced and $x_2$ the number of mugs produced. It takes $3$ hours of labor and $4$ pounds of clay to produce one bowl, and $2$ hours of labor and $1$ pound of clay to produce one mug. The firm has $60$ hours of labor and $50$ pounds of clay per day.

If the firm produces $10$ bowls and $10$ mugs, which of the following is correct?

Slack in the labor constraint is $0$ ; Slack in the clay constraint is $0$

Slack in the labor constraint is $10$ ; Slack in the clay constraint is $10$

Slack in the labor constraint is $20$ ; Slack in the clay constraint is $0$

$-$Slack in the labor constraint is $10,$ Slack in the clay constraint is $0$