The 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 - x²; C(x) = 65x + 3150; 0 less than or equal to x less than or equal to 100.

1) The manufacturer must produce ____ units to break even.

Solution

at breakeven point, C(x)=R(x)

200x - x² = 65x + 3150

solving this quadratic ,we get x=30 or 105.since 105 is outside range of x, 105 is neglected.

so at breakeven point, 30 units must be produced.