C(x) = 1600 + 1500
nonsense
nonsense
also nonsense
and by the way x*x is usually written x^2
The total cost function is given as C(x) = 1600 + 1500
The total revenue function is given as R(x) = -1600x - x^2
Setting these two equal, we have:
1600 + 1500 = -1600x - x^2
Rearranging the equation, we get:
x^2 + 1600x + 3100 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 1600, and c = 3100. Substituting these values into the formula, we get:
x = (-1600 ± √((1600)^2 - 4(1)(3100))) / 2(1)
Now we can simplify and calculate two possible solutions for x:
x = (-1600 ± √(2560000 - 12400)) / 2
x = (-1600 ± √(2547600)) / 2
x = (-1600 ± 1595.29) / 2
Therefore, the two possible solutions are:
x = (-1600 + 1595.29) / 2 ≈ -2.855
x = (-1600 - 1595.29) / 2 ≈ -3197.855
However, in this case, we are looking for the breakeven point, which represents the number of units sold. Since the number of units cannot be negative, we discard the negative solution.
Therefore, the breakeven point is approximately 2.855 units (rounded to 3 units).