The revenue function r(x) and the cost function c(x) for a particular product ar

Question

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.

Explanation / Answer

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

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