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= ?0.3802 and b₂= 0.0198, what is the level that will maximize his average cost in units?

Question

Quizplus · Accepted Answer

The quadratic regression model for cost can be represented as $C = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the number of units. The formula to find the vertex (maximum or minimum point) of a quadratic equation is given by $x = -\frac{b}{2a}$. In this context, $a = 0.0198$ and $b = -0.3802$. Substituting these values into the vertex formula gives $x = -\frac{-0.3802}{2 \times 0.0198} = 9.60$. Therefore, the level that maximizes the average cost in units is 9.60 million units.

Todd Uses the Quadratic Regression Model to Determine the Predictive