A manufacture finds the total cost "C" for a product is expressed by C=3x2-8, and the total revenue "R" by R=3x-2, where x is the number of units sold. What is the breakeven point (where total cost=total revenue) to the nearest unit?
http://www.jiskha.com/display.cgi?id=1428740268
Thank you I didn't see that !
If you stick to the same name, it is easy to find your previous posts.
Just click on your name in the list.
To find the breakeven point, we need to set the total cost (C) equal to the total revenue (R) and solve for x.
Given:
Total cost (C) = 3x^2 - 8
Total revenue (R) = 3x - 2
Setting C equal to R:
3x^2 - 8 = 3x - 2
Rearranging and combining like terms:
3x^2 - 3x - 6 = 0
Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where:
a = 3
b = -3
c = -6
To solve this quadratic equation, we can use the quadratic formula, which states:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation:
x = (-(-3) ± √((-3)^2 - 4(3)(-6))) / (2(3))
x = (3 ± √(9 + 72)) / 6
x = (3 ± √81) / 6
x = (3 ± 9) / 6
We have two possible solutions:
x = (3 + 9) / 6 = 12 / 6 = 2
x = (3 - 9) / 6 = -6 / 6 = -1
Since the number of units sold cannot be negative, we discard the negative solution.
Therefore, the breakeven point is x = 2 units (to the nearest unit).