Question

To find the number of units that gives break-even for the product, solve the equation R C. Round your answer to the nearest whole unit A manufacturer has total revenue given by the function R =258x and has total cost given by C=26x+974000 where x is the number of units produced and sold. A, 285 unitsB.3430 unitsC. 4198 unitsD. 232 units

Answer 1

From the statement of the problem, we know that:

• The revenue is given by:

`R(x)=258x,`

• The total cost is given by:

`C(x)=26x+974000.`

Where x is the number of units produced and sold.

The manufacturer will break even when the revenue is equal to the total cost:

`\begin{gathered} R(x)=C(x), \\ 258x=26x+974000. \end{gathered}`

Solving the last equation for x, we get:

`\begin{gathered} 258x-26x=974000, \\ 232x=974000, \\ x=(974000)/(232), \\ x\cong4198. \end{gathered}`

The manufacturer will break even when the number of units is 4198.

Answer

C. 4198 units