Question

A specialty muffin company makes muffins for $0.12 per muffin. The starting cost of the company is $300. How many muffins must the company make before the average cost per muffin is $0.25? Round your answer to the nearest whole number.

Answer 1

Answer:

the company should make 2307 muffins before the Average cost reaches $0.25/muffin

Step-by-step explanation:

the total cost of making the muffins is

Total cost = fixed cost + variable cost = $300 + $0.12 / muffin *Q

where Q = number of muffins

the average cost is

Average cost = Total cost / number of muffins = ($300 + $0.12 *Q) / Q =  $300/Q + $0.12 / muffin

then for Average cost=  $0.25/muffin

$300/Q + $0.12 / muffin =  $0.25/muffin

Q = $300 / ( $0.25/muffin- $0.12 / muffin ) = 2307.69 muffins ≈ 2307 muffins ( we are rounding down since we want to find the number before the cost goes below 0.25)

then the company should make 2307 muffins before the Average cost reaches $0.25/muffin

Answer 2

Answer: The company must make 2,307 muffins before the average cost per muffin becomes $0.25

Step-by-step explanation:

Now, before we can calculate the number of muffins that the company must make to bring the average cost of producing one muffin to $0.25, we have to assign a letter to that unknown variable to enable ease of calculation.

So, let the number of muffins which the company must make be "m".

If one muffin costs $0.12 to make, then the cost to make that unknown number of muffins (m) will be:

0.12 × m = $0.12m

Adding this cost to the starting cost of the company and then dividing the result by that unknown number of muffins should bring the average cost of making a muffin to $0.25

That is:

($0.12m + $300)/m

= $0.25

The next step is to make "m" the subject of the formula and then we will consequently discover the quantity of muffins to make in order to bring the average cost of producing a muffin to $0.25

Cross multiplying the equation above, we will have:

$0.12m + $300 = $0.25m

$0.25m - $0.12m = $300

$0.13m = $300

m = $300 / $0.13

m = 2,307

"m" is 2,307 muffins.

Therefore the company must make 2,307 muffins before the average cost per muffin becomes $0.25