Question

A company is selling toothpicks. It costs $0.03 to produce each toothpick and a fixed cost of $110 a month for the company. If the company is selling toothpicks for $0.04 each, how many toothpicks must they sell a month in order to break-even

Answer 1

11,000 toothpicks must be sold in order to break even.

Step-by-step explanation:

Here, let us assume the number of toothpicks sold to break even = m

So, for m toothpicks, Total cost  = Total Earnings

Now, the cost of producing 1 toothpick = $0.03

So, cost of production of m toothpicks  = m x ( cost of 1 toothpick)

= $(0.03 m)

Also, fixed month cost  = $110

So, Total cost of production = $110 + $0.03 m  .... (1)

Again, the selling cost of 1 toothpick = $0.04

So, selling cost of m toothpicks  = m ( cost of 1 toothpick)   = $(0.04 m)  ..(2)

From (1) and (2)

110 + 0.03 m = (0.04 m)

⇒ 110 = 0.01 m

or, m  = $\frac{110}{0.01} = 11,000$

⇒ m = 11,000

Hence, 11,000 toothpicks must be sold in order to break even.

Answer 2

Answer:

Company must sell 11,000 toothpicks in order to break-even.

Step-by-step explanation:

Given:

Cost to produce each toothpicks = $0.03

Fixed cost = $110

Selling price of each toothpicks = $0.04

We need to find the number of toothpicks company must sell in order to break-even.

Solution:

Let the number of tooth picks sold be 'x'.

Now we can say that;

Total cost of the company is equal to Cost to produce each toothpicks multiplied by number of tooth picks sold plus the Fixed cost

framing in equation form we get;

Total cost of the company = $0.03x+110$

Now we can say that;

Revenue generated is equal to Selling price of each toothpicks  multiplied by number of tooth picks sold.

framing in equation form we get;

Revenue generated = $0.04x$

Now we know that;

Break even point is the point at which The total cost to the company is equal to revenue generated.

So we can frame it as;

$0.03x+110=0.04x$

Combining the like terms we get;

$0.04x-0.03x=110\\\\0.01x=110$

Dividing both side by 0.01 we get;

$\frac{0.01x}{0.01}=\frac{110}{0.01}\\\\x=11,000$

Hence Company must sell 11,000 toothpicks in order to break-even.