Question

A candy company sells cases of chocolate bars. the company has cost of $30,000 and each case of chocolate bars cost an additional $5 to make. the company sells each case for a $10. the graph of a system of equations representing this company's cost and revenue, for manufacturing and selling x cases of chocolate bars is shown.how many cases of chocolate bars will the company need to sell in order for costs and revenue to be equal.

Answer 1

We have two functions:

- The cost function C(x) that can be described as the fixed cost ($30,000) plus the variable cost (the unit variable cost per unit times the units, 5x)

`C(x)=30000+5x`

- The revenue function R(x) which is the price times the number of units.

`R(x)=10x`

We have to find x for which cost and revenue are the same.

This can be expressed mathematically as C(x) = R(x).

We then can solve it as:

`\begin{gathered} C(x)=R(x) \\ 30000+5x=10x \\ 30000=10x-5x \\ 30000=5x \\ x=(30000)/(5) \\ x=6000 \end{gathered}`

This means that the company has to sell x = 6000 chocolate bars to break even (costs = revenue).

Answer: 6000 chocolate bars.