Chapter 8.2, Problem 47E

(a)

To determine

To calculate: The value and interpretation of $\frac{\partial M}{\partial c}$ and $\frac{\partial M}{\partial f}$ when the fraction of Mazda car owners who chose another new Mazda can be modeled by the function $M\left(c,f,g,h,t\right)=1.1-3.8c+2.2f+1.9g-1.7h-1.3t$. Here, $c$ is the fraction of Chrysler car owners who remained loyal to Chrysler, $f$ is the fraction of Ford car owners remaining loyal to Ford, $g$ is the corresponding figure for General Motors, $h$ is the corresponding figure for Honda, and $t$ for Toyota.

(b)

To determine

To calculate: The percentage of Mazda owners who remained loyal to Mazda when one year it was observed that $c=0.56,f=0.56,g=0.72,h=\text{0}\text{.50}$ and $t=0.43$ if the fraction of Mazda car owners who chose another new Mazda can be modeled by the function $M\left(c,f,g,h,t\right)=1.1-3.8c+2.2f+1.9g-1.7h-1.3t$ where $c$ is the fraction of Chrysler car owners who remained loyal to Chrysler, $f$ is the fraction of Ford car owners remaining loyal to Ford, $g$ is the corresponding figure for General Motors, $h$ the corresponding figure for Honda, and $t$ for Toyota.