Answer
$480$ Model-A, $240$ Model-B.
Work Step by Step
a. Assume the number of Model-A is $x$ and the number of Model-B is $y$. The objective function that models total profit can be written as $z=25x+40y$
b. Using the given constraints, we have
$\begin{cases} 0.9x+1.8y\leq864 \\ 0.8x+1.2y\leq672\\x\geq0,y\geq0 \end{cases}$
c. We can graph the inequalities as shown with the solution region and vertices
$(0,0),(0,480),(480,240),(840,0)$.
d. With the identified vertices, we have
$z_1=25(0)+40(0)=0$,
$z_2=25(0)+40(480)=19,200$,
$z_3=25(480)+40(240)=21,600$,
$z_4=25(840)+40(0)=21,000$, dollars.
e. We can identify that a maximum profit of $21,600$ dollars can be obtained when $x=480, y=240$
