Question

The revenue R

from the sale of x
cameras is given by R=46x−x2.
The cost C
of producing x
cameras is given by C=20+37x.
How many cameras must be produced and sold in order to break even? If there is more than one break-even point, separate the answers with commas.

Answer 1

To break even, either 4 or 5 cameras must be produced and sold.

Step-by-step explanation:

To break even, the revenue must be equal to the cost. So, we can set the equations for revenue and cost equal to each other and solve for x:

Revenue: R = 46x - x^2

Cost: C = 20 + 37x

Setting the equations equal to each other:

46x - x^2 = 20 + 37x

To solve for x, we need to rearrange the equation:

x^2 - 9x + 20 = 0

Factoring the equation:

(x - 5)(x - 4) = 0

Setting each factor equal to zero and solving for x:

x - 5 = 0 or x - 4 = 0

x = 5 or x = 4

So, to break even, either 4 or 5 cameras must be produced and sold.