c(x)=125x+1500andr(x)=1500x-1000



Given a cost function of C(x)=125x+1500 and a revenue function of R(x)=1500x-1000, calculate the break-even point,

Calculate the break-even point
Break-even is where C(x) = R(x)
125x+1500 = 1500x-1000

Subtract 125x from each side of the equation:
125x + 1500 - 125x = 1500x - 1000 - 125x

Cancelling the 125x on the left side, we get:
1375x - 1000 = 1500

Now add 1000 to each side:
1375x - 1000 + 1000 = 1500 + 1000

Cancelling the 1000 on the left side, we get:
1375x = 2500

Divide each side of the equation by 1375
1375x
1375
=
2500
1375

Cancelling 1375 on the left side, we get:
1375x
1375
=
2500
1375

x = 8 ← This is the break-even quantity.

Given the break even quantity x = 8, calculate the break even amount using the revenue function R(x)
R(8) = 1500(8) - 1000
R(8) = 127