The number of solutions in a linear programming model to maximize $5x+4y$ subject to $x-2y\ge 2$, $2x-4y\le -3$, and $x,y\ge 0$ will be:

Let's analyze the constraints:$x-2y\ge 2⟹x-2y=2$ passes through $(2,0)$ and $(0,-1)$.$2x-4y\le -3⟹2x-4y=-3⟹x-2y=-1.5$.Notice that the lines $x-2y=2$ and $x-2y=-1.5$ are parallel.For the first constraint, $x-2y\ge 2$.For the second constraint, $x-2y\le -1.5$.There is no value of $(x-2y)$ that can be simultaneously $\ge 2$ and $\le -1.5$.Thus, there is no feasible region. The number of solutions is zero.