Question

A company manufactures a certain item and sells it online. The company has a business model where the cost C, in dollars, to make x items is given by the equation C=2.5x+21 and the revenue R, in dollars, made by selling x items is given by the equation R=6x. The break even point is the point where the cost and the revenue intersect. How many items must the company sell to break even?

Answer 1

Answer:

see the attachment

Step-by-step explanation:

The break-even point is on both curves. The y-intercept can be used for the other point in each case.

The break-even point is where cost and revenue are the same:

 20/3x +50 = 10x

 50 = 10/3x . . . . . . . . subtract 20/3x

 15 = x . . . . . multiply by 3/10

 r = c = 10(15) = 150 . . . . for x = 10

Two points you can use for graphing the lines are ...

 cost: (0, 50) and (15, 150)

 revenue: (0, 0) and (15, 150)

Answer 2

9514 1404 393

Answer:

  6

Step-by-step explanation:

Cost and revenue are equal when ...

  C = R

  2.5x +21 = 6x

  21 = 3.5x . . . . . . subtract 2.5x

  6 = x . . . . . . . . . .divide by 3.5

The company must sell 6 items to break even.