The total cost of the factory will be the sum of its variable costs and it's fixed costs. The factory has fixed costs of $53,900 and variable costs of $12.50 per unit produced. Let [tex]x[/tex] be the number of toy's produced by this Toby's Tiny Toys, then the total variable costs will be [tex]12.50x[/tex]. From this information we can gather that the cost function for this factory is,
[tex]C(x)=53\,900+12.50x.[/tex]
On the other hand, if we let [tex]x[/tex] be the number of toys sold, we can gather that at the selling price of 16.50, the revenue function will be ,
[tex]R(x)=16.50x.[/tex]
Toby's Tiny Toys will reach their break even point when the total costs are equal to the total revenue. At this break even point ,we have that
[tex]R(x)=C(x)\\\implies 16.50x=12.50x+53\,900\\\implies 16.50x-12.50x=53\,900\\\implies 4x=53\,900\\\implies x=\frac{53\,900}{4} \\\implies x=134\,750.[/tex]
The company has to sell 134 750 units to break even.
