If the production function is f(x, y) min12x, 3y, then there is convexity in production.

If the production function satisfies the property of convexity, then it should satisfy the following condition:
f(αx1+(1-α)x2, αy1+(1-α)y2) ≤ αf(x1, y1) + (1-α)f(x2, y2)
where α is a scalar parameter between 0 and 1, and (x1,y1) and (x2,y2) are two different input combinations.
In this case, we can verify that the production function satisfies the above condition for any values of (x1,y1) and (x2,y2), and for any value of α between 0 and 1. Therefore, we can conclude that the production function is convex.