Question

The revenue for selling a units of a product is R = 40x. The cost of producing x units is C = 20 + 7700.In order to obtain a profit, the revenue must be higher than the cost, so we want to know, for what values of a will this product return a profit.To obtain a profit, the number of units must be greater than _____

Answer 1

Step-by-step explanation:

We are given the revenue function and the cost function for x units of a product as follows;

`\begin{gathered} Revenue=40x \\ Cost=20x+7700 \end{gathered}`

We are also told that to obtain a profit, the revenue must be higher than the cost. This means;

`\begin{gathered} Profit: \\ R(x)>C(x) \end{gathered}`

To determine which unit(s) of x will yield a profit, we can now substitute the values into the equation above;

`\begin{gathered} Profit: \\ 40x>20x+7700 \end{gathered}`
`\begin{gathered} Profit: \\ 40x-20x>7700 \end{gathered}`

`\begin{gathered} Profit: \\ 20x>7700 \end{gathered}`

Divide both sides by 20;

`(20x)/(20)>(7700)/(20)`

`x>385`

For this answer, we know that to make a profit, the units produced must be greater than 385 units.

ANSWER:

To obtain a profit the number of units must be greater than 385