# The cost to produce x units of lipstick is c(x)=60x+10000 while the revenue is R(x)=85x Find: a. Break-even point b. Revenue at break-even point

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### 2 Answers

The cost to produce x unit of lipstick is given as c(x) = 60x + 10000 and the revenue is r(x) = 85x

If the break even is at N

c(N) = r(N)

=> 60*N + 10000 = 85*N

=> 25N = 10000

=> N = 10000/25

=> N = 400

The revenue at break even is 85*400 = 34000

**Break-even point = 400 lipsticks. **

**Revenue at break-even = 34000.**

The cost function is given by c(x) = 60x+10000

The revenue fuctionÂ is given by: R(x) = 85x.

To determine the break even point, we set cost = revenue and solve for x.

=> At he break even point c(x) = R(x).

=> 60x+10000 = 85x

=> 10000 = 85x- 60x = 25x.

=> 10000/25 = 25x/25.

=> **x = 400 **is the break even point.

b) To find break even revenue, we put x= 400 in R(x).

R(x) = 85x

So break even revenue = R(400) = 85*400 = **34000.**

**Break even point = 400 units. Break even revenue = 34000 units of money.**