1. The reproduction function for a certain North American species of duck is estimated to be f(p) = −.02p^2 + 7p, where p and f (p are measured in thousands. Find the size of the population that allows the maximum sustainable yield, and also find the size of the yield.
2. Economists have found that if cigarettes are taxed at a rate t, then the cigarette sales will be S(t) = (64−51.26t)/ (1 +t) (billions of dollars annually, before taxes). Remembering that tax revenue is tax rate times sales, find the tax rate that maximizes government revenue on cigarette sales.