Todd uses the quadratic regression model to determine the predictive average unit cost of baseballs produced in his production facility. After determining predictive average costs at multiple unit batch size amounts in millions, he now wants to know what the output level that minimizes his costs would be.
-Given b₁ = -0.3600 and b₂ = 0.0201, what is the level that will maximize his average cost in units?

Question

Quizplus · Accepted Answer

The output level that minimizes cost in a quadratic equation of the form $y = ax^2 + bx + c$ is found at the vertex of the parabola, which is given by the formula $x = -\frac{b}{2a}$. In this context, $a = 0.0201$ and $b = -0.3600$, so substituting these values into the formula gives $x = -\frac{-0.3600}{2 \times 0.0201} = \frac{0.3600}{0.0402} = 8.9552$, which rounds to approximately 8.96 million units.

Todd Uses the Quadratic Regression Model to Determine the Predictive