A factory has a fixed cost of $45,000 a month, and a cost

Hi VJesus12,

We're told that a factory has a fixed cost of $45,000 a month, a cost of $2.50 for every item produced and a selling price of a single item is $5. We're asked for the number of items that must be sold each month for the factory to cover its costs exactly. This question can be solved in a couple of different ways, depending on how you choose to do the math. Here's how you can use a little math - and some estimation (along with the 'spread' of the answer choices) - to get to the correct answer.

To start, each item sold has a profit of $5 - $2.50 = $2.50

Selling 10,000 items would get you a profit of... ($2.50)(10,000) = $25,000
Selling 20,000 items would get you a profit of... ($2.50)(20,000) = $50,000

We need to cover the fixed cost of $45,000, so the number of items sold has to be LESS than 20,000... but closer to 20,000 than it is to 10,000. There's only one answer that matches....

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote:A factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?

A. 9,000
B. 14,000
C. 18,000
D. 22,500
E. 27,000

The OA is the option C.

Why is not the option A correct? I am confused here. Experts, can you help me? Thanks.

We can create the equation:

45,000 + 2.5n = 5n

45,000 = 2.5n

18,000 = n

Alternate Solution:

The company makes a profit of 5 - 2.5 = $2.5 per item. Therefore, to cover the cost of $45,000; the company must sell 45000/2.5 = 18,000 items.

Answer: C