# 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

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.