Answer
More than $1200$ packages must be produced.
Work Step by Step
Let the number of packages of stationery each week be $x$.
The weekly fixed cost is $\$3,000$ plus $\$3.00$ per package.
The weekly selling price is $\$5.50$ per package.
In the mathematical form.
The weekly fixed cost $=3,000+3.00x$.
The weekly selling price $=5.50x$.
The inequality for the company profit is
The weekly selling price $>$ The weekly fixed cost.
The inequality is
$\Rightarrow 5.50x>3,000+3.00x$.
Add $-3.00x$ to both sides.
$\Rightarrow 5.50x-3.00x>3,000+3.00x-3.00x$.
Simplify.
$\Rightarrow 2.50x>3,000$.
Divide both sides by $2.50$.
$\Rightarrow \frac{2.50x}{2.50}>\frac{3,000}{2.50}$.
Simplify.
$\Rightarrow x>1200$.
Hence, more than $1200$ packages must be produced.
