Question

The manufacturer of an energy drink spends $1.20 to make each drink and sells them for two dollars the manufacturer also has fixed costs each month of $8000 find the number of energy drinks X that the manufacturer needs to sell in order to break even

Answer 1

Given:

The cost of a energy drink is $1.20.

The manufacturing fixed cost is $8000.

The selling cost of a drink is $2 for each.

Step-by-step explanation:

The cost function includes energy drink cost and fixed cost. So cost function for x energy drink is,

`C(x)=1.20x+8000`

The revenue function for the x energy drinks is,

`R(x)=2.0x`

For break-even point the cost function and revenue functions are equal. So,

`1.20x+8000=2.0x`

Simplify the equation to obtain the value of x.

`\begin{gathered} 1.20x+8000=2.0x \\ 2.0x-1.20x=8000 \\ x=(8000)/(0.8) \\ =10000 \end{gathered}`

So number of energy drinks need to sell for break even is 10000.