Question

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.

C(x) = 4000x + 88,000
R(x) = 12,000x

Answer 1

Equate the functions and then solve for x.

`</p><p>C(x)=R(x) \\</p><p>4\cdot10^3x+88\cdot10^3 = 12\cdot10^3x \\</p><p>88\cdot10^3=12\cdot10^3x-4\cdot10^3x \\</p><p>88\cdot10^3=8\cdot10^3x \\</p><p>x=(88\cdot10^3)/(8\cdot10^3)=(88)/(8)=\boxed{11}</p><p>`

Hope this helps.

Answer 2

Answer: 11 units must be sold to break even.

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