Equate the functions and then solve for x.
[tex]
C(x)=R(x) \\
4\cdot10^3x+88\cdot10^3 = 12\cdot10^3x \\
88\cdot10^3=12\cdot10^3x-4\cdot10^3x \\
88\cdot10^3=8\cdot10^3x \\
x=\dfrac{88\cdot10^3}{8\cdot10^3}=\dfrac{88}{8}=\boxed{11}
[/tex]
Hope this helps.
Answer: 11 units must be sold to break even.
Step-by-step explanation:
Profit is expressed as Revenue - Cost. Break even is the point at which there is neither profit nor loss. This means that profit would be zero. Therefore,
Revenue - cost = 0
Revenue = cost
Given the cost function, C(x) to be
C(x) = 4000x + 88,000
and the revenue function, R(x) to be
R(x) = 12,000x, the number of units x that must be sold to break even would be
4000x + 88000 = 12000x
12000x - 4000x = 88000
8000x = 88000
x = 88000/8000 = 11
