A hoverboard manufacturer has just announced the Glide 5 hoverboard. The accounting department has determined that the cost to manufacturer the Glide 5 hoverboard and the equation is
y
=
35.78
x
+
31842
. The revenue equation is
y
=
87.98
x
.
What is the break-even point for the Glide 5 hoverboard?
The break even point for the Glide 5 hoverboard is
.
(Round x to the nearest whole number and y to two decimal places.)
To find the break-even point, we need to determine the point at which the cost to manufacture the Glide 5 hoverboard is equal to the revenue generated by selling it.
The cost equation is given as:
y = 35.78x + 31842
And the revenue equation is:
y = 87.98x
At the break-even point, the cost (y) and the revenue (y) will be equal.
Setting the cost equation equal to the revenue equation, we have:
35.78x + 31842 = 87.98x
Subtracting 35.78x from both sides of the equation, we get:
31842 = 52.2x
Dividing both sides of the equation by 52.2, we have:
x = 610.69
Rounding x to the nearest whole number, the break-even point for the Glide 5 hoverboard is approximately 611.
To find the corresponding y value, we substitute the value of x into the revenue equation:
y = 87.98 * 611 = 53601.78
Rounding y to two decimal places, the break-even point for the Glide 5 hoverboard is approximately $53,601.78.
To find the break-even point for the Glide 5 hoverboard, we need to find the value of x at which the cost (y) equals the revenue (y).
Since the cost equation is y = 35.78x + 31842, and the revenue equation is y = 87.98x, we can set them equal to each other:
35.78x + 31842 = 87.98x
Now, let's solve for x:
Subtract 35.78x from both sides:
31842 = 52.2x
Divide both sides by 52.2:
x = 31842 / 52.2
x ≈ 610.69
Since we need to round x to the nearest whole number, the break-even point for the Glide 5 hoverboard is approximately 611 units.
To calculate the corresponding cost (y), substitute the value of x back into either the cost or revenue equation. Using the revenue equation, we can find the revenue at the break-even point:
y = 87.98 * 611
y ≈ 53716.78
Rounded to two decimal places, the break-even revenue for the Glide 5 hoverboard is approximately $53,716.78.
35.76x + 31842 = 87.98x.
X =