Answer
a) $W$ decreases as $T$ increases; $W$ increases as $R$ increases.
b) $-1.1$
Work Step by Step
a) Here, $W_T \lt 0$. This means that the rate of change of wheat production (W) with respect to the average temperature (T) is negative. This implies that $W$ decreases as $T$ increases.
Here, $W_R \gt 0$. This means that the rate of change of wheat production (W) with respect to the annual rainfall (R) is positive. This implies that $W$ increases as $R$ increases.
(b) We need to use the chain rule.
$\dfrac{dW}{dt}=(\dfrac{\partial W}{\partial T})(\dfrac{dT}{ dt})+(\dfrac{\partial W}{\partial R})(\dfrac{dR}{ dt})=(-2) \times (0.15)+(8) \times (-0.1)$
Hence, we have $\dfrac{dW}{dt}=-(0.3)-(0.8)=-1.1$
