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 fuction 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.