Homework SourseThe revenue function rx and the cost function cx for a parti
The revenue function r(x) and the cost function c(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even.
R(x) =200x-2x^2; C(x)=-x^2+15x+8250; 0<x<100
The manufacturer must produce ____ units to break even.
The revenue function r(x) and the cost function c(x) for a particular product are given. These functions are valid only for the specified range of values. Find the number of units that must be produced to break even.
R(x) =200x-2x^2; C(x)=-x^2+15x+8250; 0<x<100
The manufacturer must produce ____ units to break even.
R(x) =200x-2x^2; C(x)=-x^2+15x+8250; 0<x<100
The manufacturer must produce ____ units to break even.
Solution
at beakeven points revenue function is equal to cost function
R(x) = C(x)
200x-2x^2 = -x^2+15x+8250
add 2x^2 on both sides
200x = x^2 + 15x + 8250
subtracting 200x from both sides
x^2 - 185x + 8250 = 0
on solving the equation we get
( x - 75)( x - 110) = 0
x = 110
x = 75
since range of x is 0 to 100
hence we discard x = 110
the manufacturer must produce 75 units to breakeven
