#### Answer

40 Model-A and 0 Model-B bikes.

#### Work Step by Step

Step 1. Assume $x$ number of Model-A and $y$ number of Model-B are produced.
Step 2. Based on the given conditions, the total profit can be written as $z(x,y)=25x+15y$
Step 3. We can convert the constraints into inequalities
as $\begin{cases} 5x+4y\leq200\\2x+3y\leq108 \end{cases}$
Step 4. See graph for the vertices and the solution region as a four-sided area.
Step 5. With the objective equation and vertices, we have
$z(0,0)=25(0)+15(0)=0$, $z(0,36)=25(0)+15(36)=540$, $z(24,20)=25(24)+15(20)=900$, $z(40,0)=25(40)+15(0)=1000$
Step 6. Based on the above results, we can find the maximum profit as $z(40,0)= 1000$ dollars by producing 40 Model-A and 0 Model-B bikes.