Daren is opening a store that sells wooden mats. He invested $10 for marketing and raw materials cost $8 for each mat he makes. Daren can sell his mats for $9 per mat. He will break even once he makes and sells a certain number of mats, with identical expenses and sales. What would the total expenses and sales be then? How many mats would that take?

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elcharly64 elcharly64 · Answer 1 · 2020-10-25T15:08:44+01:00

Answer:

The total expenses and sales will be $90 and it would take 10 mats

Step-by-step explanation:

Equations

This problem can be solved by pure logical deduction, but we'll use equations instead.

Daren has a cost structure made of a fixed investment of $10 and a variable cost of $8 per mat he makes.

The total cost function can be written as:

C(x)=10+8x

Where x is the number of mats made.

Daren can sell the mats for $9 each. The revenue function is:

R(x)=9x

The number of sold mats needed to break even will occur when cost and revenue are the same:

10+8x=9x

Solving:

x=10 mats

The cost of 10 mats is:

C(10)=10+8*10=$90

The revenue for 10 mats is:

R(10)=9*10=90

The total expenses and sales will be $90 and it would take 10 mats