Exercise 36

Wheat production \(W\) in a given year depends on the average temperature \(T\) and the annual rainfall \(R\). Scientists estimate that the average temperature is rising at a rate of 0.15°C/year and rainfall is decreasing at a rate of 0.1 cm/year. They also estimate that at current production levels, \(\partial W / \partial T = -2\) and \(\partial W / \partial R = 8\). (a) What is the significance of the signs of these partial derivatives? (b) Estimate the current rate of change of wheat production, \(dW/dt\).