Answer
$10$ Boeing 727s and $42$ Falcon 20s.
Work Step by Step
Step 1. Assume that $x$ Boeing 727 and $y$ Falcon 20 are needed.
Step 2. Based on the given conditions, the total number as $z(x,y)=x+y$
Step 3. We can convert the constraints into inequalities as
$\begin{cases} x\geq0,y\geq0\\1400x+500y\leq35000\\42000x+6000y\geq672000\\x\leq20\end{cases}$
Step 4. Graphing the above inequalities, we can find the vertices and the solution region as a four-sided area.
Step 5. With the objective equation and vertices, we have $z(16,0)=16+0=16$, $z(10,42)=10+42=52$, $z(25,0)=25+0=25$,
Step 6. Based on the above results, we can find the maximum as $z(10,42)=10+42=52$, with $10$ Boeing 727s and $42$ Falcon 20s.
