Respuesta :
Given:
Cost function, C(x) and revenue function, R(x) are
[tex]C(x)=150x+30000[/tex]
[tex]R(x)=400x[/tex]
To find:
The break-even point.
Solution:
We know that, at break-even point the cost is equal to revenue.
Equate cost function and revenue function to get the break-even point.
[tex]C(x)=R(x)[/tex]
[tex]150x+30000=400x[/tex]
[tex]30000=400x-150x[/tex]
[tex]30000=250x[/tex]
Divide both sides by 250.
[tex]\dfrac{30000}{250}=x[/tex]
[tex]120=x[/tex]
Put x=120 in R(x).
[tex]R(120)=400(120)[/tex]
[tex]R(120)=48000[/tex]
It means, the revenue and cost are equal, i.e., 48000 at x=120.
Therefore, the break even point is x=120.
120 units of products are required to break even.
Revenue is the amount of money that can be made from selling a particular number of items while cost is the amount of money used to produce those items.
At breakeven point, revenue and cost are the same,
Let x represent the number of units produced. hence at break even:
Revenue = cost
R(x) = C(x)
400x = 150x + 30000
250x = 30000
x = 120 units
Therefore 120 units of products are required to break even.
Find out more at: https://brainly.com/question/15356272