The total profit function, P(x), for a company producing x thousand units is given by P(x)=−2x^2+38x−120. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x)0.] Explain and justify your answer.

Question

The total profit function,​ P(x), for a company producing x thousand units is given by P(x)=−2x^2+38x−120. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x)>0.] Explain and justify your answer.

oobleck · Answer

−2x^2+38x−120 P=0 at x=4,15 Since the parabola opens downward, the vertex is above the x-axis., P(x) is positive between these values.

The total profit function,​ P(x), for a company producing x thousand units is given by P(x)=−2x^2+38x−120. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x)>0.] Explain and justify your answer.

The total profit function, P(x), for a company producing x thousand units is given by P(x)=−2x^2+38x−120. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x)>0.] Explain and justify your answer.