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

Answer:

397 bikes

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:

$\begin{gathered} 246.15x-120>50,000 \\ 126.15x>50,000 \\ \frac{126.15x}{126.15}>\frac{50,000}{126.15} \\ x>396.4 \end{gathered}$

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