Answer
More than $6250$ DVDs must be produced.
Work Step by Step
Let the number of DVDs produced each week be $x$.
The weekly cost price of the DVDs is $\$10,000$ plus $\$0.40$ per DVDs.
The weekly selling price of the DVDs is $\$2.00$ per DVDs.
In the mathematical form.
The weekly cost price $=10,000+0.40x$.
The weekly selling price $=2.00x$.
The inequality for the company profit is
The weekly selling price $>$ The weekly cost price.
The inequality is
$\Rightarrow 2.00x>10,000+0.40x$.
Add $-0.40x$ to both sides.
$\Rightarrow 2.00x-0.40x>10,000+0.40x-0.40x$.
Simplify.
$\Rightarrow 1.60x>10,000$.
Divide both sides by $1.60$.
$\Rightarrow \frac{1.60x}{1.60}>\frac{10,000}{1.60}$.
Simplify.
$\Rightarrow x>6250$.
Hence, more than $6250$ DVDs must be produced.
