Question

Finding the Break-Even Point and the Profit Function Using Substitution Given the cost function C(x)=0.85x+35,000 and the revenue function R(x)=1.55x,find the break-even point and the profit function?

Answer 1

`x=50000`

`P(x)=0.7x-35000`

Explanation:

Given cost function is

`C(x)=0.85x+35000`

and revenue function is

`R(x)=1.55x`

At break even point, revenue is equal to cost

R(x)= C(x)

`1.55x=0.85x+35000`

Subtract 0.85 from both sides

`0.7x=35000`

divide by 0.7 on both sides

`x=50000`

Profit function

P(x)= R(x)- C(x)

`P(x)=1.55x-(0.85x+35000)`

`P(x)=1.55x-0.85x-35000`

`P(x)=0.7x-35000`