if a compañy has total costs C(x) = 1600 + 1500 and total revenues are R(x) -0 1600x-x2, find the breack-even point
C(x) = 1600 + 1500
nonsense
R(x) -0 1600x-x2
also nonsense
and by the way x*x is usually written x^2
To find the breakeven point, we need to set the total revenue equal to the total cost and solve for x.
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).