Question

A producer of felt-tip pens has received a forecast of demand of 31,000 pens for the coming month from its marketing department. Fixed costs of $25,000 per month are allocated to the felt-tip operation, and variable costs are 40 cents per pen. Find the break-even quantity if pens sell for $4 each. (Round your answer to the next whole number.)

Answer 1

Answer: the break-even quantity is 6944

Explanation:

Let x represent the break-even quantity.

Fixed costs of $25,000 per month are allocated to the felt-tip operation, and variable costs are 40 cents(40/100 = $0.4) per pen. This means that the total cost of producing x pens for the forth coming month would be

0.4x + 25000

if pens sell for $4 each, it means that the total revenue from selling x pens would be

4x

At the point of break even, the total cost = total revenue

Therefore,

4x = 0.4x + 25000

4x - 0.4x = 25000

3.6x = 25000

x = 25000/3.6

x = 6944 to the nearest whole number

Answer 2

6945 is the break-even quantity if pen sells for $4 each.

Explanation:

We are given the following in the question:

Demand of pens = 31,000

Fixed cost = $25,000 per month

Variable cost per pen = 40 cents = $0.4

Selling price of each pen = $4

Let q be the break even quantity,

Then we can write:

`\text{Selling price}(q) = \text{Fixrd cost} + \text{Variable cost}(q)`

Putting values, we get,

`4q = 25000 + 0.4q\\(4-0.4)q = 25000\\3.6q = 25000\\q = 6944.44 \approx 6945`

Thus, 6945 is the break-even quantity if pen sells for $4 each.