Let the points  $$\left(\frac{11}{2},\alpha\right)$$ lie on or inside the triangle with sides $$x+y=11,\; x+2y=16$$  and $$2x+3y=29.$$ Then the product of the smallest and the largest values of  $$\alpha$$  is equal to:

Substitute $$x = 5.5$$ into the boundary equations:

$$5.5 + y = 11 \implies y = 5.5$$

$$5.5 + 2y = 16 \implies 2y = 10.5 \implies y = 5.25$$

$$2(5.5) + 3y = 29 \implies 11 + 3y = 29 \implies 3y = 18 \implies y = 6$$

The vertical line $$x = 5.5$$ intersects the triangle region. The values of $$\alpha$$ must fall between the boundaries. Checking the intersection of the lines, $$\alpha$$ is bounded by $$5.5$$ and $$6$$.

Smallest value $$\alpha_{min} = 5.5$$, Largest $$\alpha_{max} = 6$$.

Product: $$5.5 \times 6 = 33$$.