The profit function for a product is given by $P ( x ) = - 0.7 x ^ { 3 } + 115.5 x ^ { 2 } - 3710 x - 84,000$ dollars, where x is the number of units produced and sold. Determine the levels of production and sale that give break-even.
A) 80 or 100 units
B) 100 units
C) 120 units
D) 90 or 120 units

Question

The profit function for a product is given by  $P ( x ) = - 0.7 x ^ { 3 } + 115.5 x ^ { 2 } - 3710 x - 84,000$ dollars, where x is the number of units produced and sold. Determine the levels of production and sale that give break-even.
A) 80 or 100 units
B) 100 units
C) 120 units
D) 90 or 120 units

Quizplus · Accepted Answer

To find the break-even points, set the profit function $P(x) = 0$ and solve for $x$. The equation becomes $-0.7x^3 + 115.5x^2 - 3710x - 84,000 = 0$. Solving this cubic equation for $x$ gives the production levels at which the profit is zero, indicating break-even points. Without explicitly solving the cubic equation here, the correct answer is based on the options provided and understanding that break-even points occur where the profit function intersects the x-axis. Given the nature of cubic functions and the options provided, 80 or 100 units are plausible break-even points for this specific profit function.

The Profit Function for a Product Is Given By P(x)=−0.7x3+115.5x2−3710x−84,000P ( x ) = - 0.7 x ^ { 3 } + 115.5 x ^ { 2 } - 3710 x - 84,000P(x)=−0.7x3+115.5x2−3710x−84,000

The Profit Function for a Product Is Given By $P ( x ) = - 0.7 x ^ { 3 } + 115.5 x ^ { 2 } - 3710 x - 84,000$