Question

the revenue R for selling X mountain bikes is R = 246.15x. the cost to produce x bikes C = 50,000 + 120 x. find the number of bikes that the company needs to sell to produce a profit

Answer 1

397 bikes

Step-by-step explanation:

The revenue function is given as:

`R=246.15x`

The cost to produce x bikes is:

`C=50,000+120x`

For the company to make a profit, the revenue must be greater than the cost.

`\begin{gathered} R(x)>C(x) \\ 246.15x>50,000+120x \end{gathered}`

Next, solve the inequality for x:

`\begin{gathered} 246.15x-120>50,000 \\ 126.15x>50,000 \\ (126.15x)/(126.15)>(50,000)/(126.15) \\ x>396.4 \end{gathered}`

Thus, if the company produces 397 bikes, they will make a profit.