find the number of units that must be produced to break even.

R(x)=200x - x^2
C(x)= 70x +2200
0 < x < 100 (These < are supposed to b less than or equal to signs)

To find the number of units that must be produced to break even, we need to set the revenue equal to the cost and solve for x.

Given:
R(x) = 200x - x^2 (revenue function)
C(x) = 70x + 2200 (cost function)
0 < x ≤ 100

To find the break-even point, we set R(x) equal to C(x):

200x - x^2 = 70x + 2200

Rearranging the equation:

x^2 - 130x + 2200 = 0

Now we can solve this quadratic equation to find the break-even point.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation: a = 1, b = -130, c = 2200

x = (-(-130) ± √((-130)^2 - 4*1*2200)) / (2*1)
x = (130 ± √(16900 - 8800)) / 2
x = (130 ± √8100) / 2
x = (130 ± 90) / 2

There are two possible solutions:
1. x = (130 + 90) / 2 = 110
2. x = (130 - 90) / 2 = 20

Since 0 < x ≤ 100, the break-even point is x = 20.

Therefore, to break even, 20 units must be produced.

To find the number of units that must be produced to break even, we need to determine the value of x when the revenue (R(x)) equals the cost (C(x)).

Given:
R(x) = 200x - x^2
C(x) = 70x + 2200

To find the break-even point, we set R(x) = C(x):

200x - x^2 = 70x + 2200

Rearrange the equation to form a quadratic equation:

x^2 + 130x - 2200 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Since the coefficient of x^2 is 1, we can factorize it relatively easily.

(x - 20)(x + 110) = 0

Solving for x, we have two possible solutions:
1) x - 20 = 0, which gives x = 20
2) x + 110 = 0, which gives x = -110

Since the given range is 0 < x < 100, we discard the negative value and only consider x = 20.

Therefore, to break even, 20 units must be produced.

Break even is when R(x) =C(x)

200x - x^2 =70x +2200

0 = x^2 -130x +2200
Factor (x-110)(x-20) = 0
x = 110 or x =20

Given the values of x stated above.
Your only possible answer is 20.