Question

The total fixed costs of producing a product is $55,000 and the variable cost is $190 per item. If the company believes they can sell 2,500 items at $245 each, what is thebreak-even point?800 items900 items960 items 1,000 itemsNone of these choices are correct.

Answer 1

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):

`\begin{gathered} TC=FC+2,500\cdot VC \\ TC=55,000+2,500\cdot190 \\ TC=530,000 \end{gathered}`

Sells:

Now, company sells eacho of the 2,500 items at $245, so, the company income (I) is:

`I=245\cdot x`

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:

`\begin{gathered} TC\text{ = I} \\ \to530,000=245\cdot x \\ \to x=(530,000)/(245)\text{ =2,163.3 (rounded) } \end{gathered}`

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".