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Wheat production in a given year, W, 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 degrees celsius per year and rainfall is decreasing at a rate of 0.1 cm per year. The also estimate that, at current production levels, ∂W/∂T = -2 and ∂W/∂R = 8.

a) what is the significance of the signs of the partials?

b) estimate the current rate of change of wheat production dW/dt.