The function to be maximized is given by $\mathrm{Z}=3 x+2 y$. The feasible region for this function is the…
The function to be maximized is given by $\mathrm{Z}=3 x+2 y$. The feasible region for this function is the shaded region given below, then the linear constraints for this region are given by
$3 x+8 y \leq 24,4 x+5 y \leq 20,5 x+3 y \geq 15$, $x \geq 0, y \geq 0$
$3 x+8 y \geq 24,4 x+5 y \geq 20,5 x+3 y \leq 15$, $x \geq 0, y \geq 0$
$3 x+8 y \leq 24,4 x+5 y \geq 20,5 x+3 y \geq 15$, $x \geq 0, y \geq 0$
$3 x+8 y \geq 24,4 x+5 y \leq 20,5 x+3 y \leq 15$, $x \geq 0, y \geq 0$
Solution
Shaded region lies origin side of $4 x+5 y \leq 20$, $5 x+3 y \leq 15$ and on non-origin side of $3 x+8 y \geq 24$.
$\begin{array}{ll}
\therefore \quad 3 x+8 y & \geq 24,4 x+5 y \leq 20,5 x+3 y \leq 15 \\
& x \geq 0, y \geq 0
\end{array}$
