A company determines that its total profit is given by the f

A company determines that its total profit is given by the function P(x) = -3x^2 + 573x - 5940 The company makes a profit for those nonnegative values of x for which P(x) > 0 The company loses money for those nonnegative values of x for which P(x)

Solution

P(x) = -3x^2 + 573x - 5940

Profit : P(x) > 0 ; -3x^2 + 573x - 5940 >0

x^2 -191x + 1980 <0

(x - 180)(x -11) <0

Solution : 11<x < 180

Losse :

x^2 -191x + 1980 <0

( x -180) ( x -11)>0

x<11 or x> 180

Profit in the interval : ( 11 , 180)