Answer
a) $W$ decreases as $T$ increases and $W$ increases as $R$ increases.
b) $-1.1$
Work Step by Step
a) 1) We can see that the rate of change of wheat production (W) w.r.t. the average temperature (T) is negative, that is, $W_T \lt 0$. This means that $W$ decreases as $T$ increases.
2) We can see that the rate of change of wheat production (W) w.r.t. the annual rainfall (R) is positive, that is, $W_R \gt 0$. This means that $W$ increases as $R$ increases.
Hence, $W$ decreases as $T$ increases and $W$ increases as $R$ increases.
b) Apply the chain rule:
$\dfrac{dW}{dt}=(\dfrac{\partial W}{\partial T})(\dfrac{dT}{ dt})+(\dfrac{\partial W}{\partial R})(\dfrac{dR}{ dt})=(-2)(0.15)+(8) (-0.1)=-0.3-0.8=-1.1$
