Let's call FC the fixed cost for production and VC the variable cost per item.
The company believes they can sell 2,500 items at $245 each.
Production costs:
For producing 2,500 items, the company has to spend (total cost, TC):
[tex]\begin{gathered} TC=FC+2,500\cdot VC \\ TC=55,000+2,500\cdot190 \\ TC=530,000 \end{gathered}[/tex]Sells:
Now, company sells eacho of the 2,500 items at $245, so, the company income (I) is:
[tex]I=245\cdot x[/tex]where x is the number of items sold.
Break-even point:
This point is reached when company can recover the money they spend (TC). So, we have the following eaquation to solve:
[tex]\begin{gathered} TC\text{ = I} \\ \to530,000=245\cdot x \\ \to x=\frac{530,000}{245}\text{ =2,163.3 (rounded) } \end{gathered}[/tex]Since company can not sell fractions of items, they have to sell 2,164 items to take back the money they invested.
So, "None of these choices are correct".
