2.Your company has determined that the profit equation (in thousands of dollars)

Question

2.Your company has determined that the profit equation (in thousands of dollars) of producing x thousand smartphones is as follows:

Profit = –x2 + 110x – 1,000

(If the number of smartphones is 40,000, for example, then x = 40). The break-even point is the number of smartphones sold and produced that would result in a profit of zero.
Use your preferred method for solving the quadratic equation to determine the break-even point. Clearly demonstrate how the answer is determined, and interpret the result in real-life terms.
This is how far I got and then became confused again.
0=x^2 + 110x - 1,000 I know I'm supposed to solve for x and am all confused again.
Thanks in advance for helping.

Explanation / Answer

As the above users have posted, the Quadratic formula is a really good way to solve this particular word problem.

With the equation that you are given, -x^2+110x-1000, you can see that
a = -1
b = 110
c = -1000

Then, you plug it in.
You will have two solutions, one with the + before the square root and one with the - before the square root.

(1) -110+ sqrt( 110^2 -4(-1)(-1000))
-----------------------------------
2(-1)

(2) -110- sqrt (110^2 - 4(-1)(-1000))
-----------------------------------
2(-1)

For solution (1), you should get -20/-2 or 10. For solution (2), you should get -200/-2 or 100.

That means that when x=10 (or 10,000 smartphones) and when x=100 (or 100,000 smartphones), the number of smartphones sold and produced is exactly the same, giving the breakeven point.

Hope this helps!

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