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

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.