U2.L3.HW: Systems of Linear Equations: Question 28

Question

A hoverboard manufacturer has just announced the Glide 5 hoverboard. The accounting department has determined that the cost to manufacture the Glide 5 hoverboard and the equation is y=35.16x+20672. The revenue equation is y=67.46x. What is the break-even point for the Glide 5 hoverboard?

Answer 1

You break even when the money you make (revenue) equals the cost it takes to produce (cost).

If revenue = cost then:

35.16x + 20672 = 67.46x (subtracting 35.16x from both sides:

20672 = 32.3x (dividing both sides by 32.3:

x = 640

So the break even point is when you produce 640 Glide 5's at which time both the revenue and cost are $43,174.40 (found by plugging in x = 640 to either revenue or cost equation)