Let the points ((11)/(2), ) lie on or inside the triangle with sides x+y=11, x+2 y=16 and …

Question

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

Accepted Answer

Point of intersection of $x=\frac{11}{2}$ with $L_1 \& L_3$ gives,

$\alpha_{\min }=\frac{11}{2}$

and $\alpha_{\max }=6$

$$\therefore \alpha_{\min } \cdot \alpha_{\max }=\frac{11}{2} \times 6=33$$

Solutions · 1