Suppose that the utility function of an enterprise consumer for coal (C) and natural gas (G) is given by U(C,G) = a In(C) + (1 - a) In (G) where 0 < a < 1. Suppose the prices of coal and gas are $2 and $4 respectively and the enterprise consumer has a yearly energy budget of $100000. Suppose in addition that the government has chosen to ration coal because of climate concerns by allowing a maximum consumption of 25000 units (C25000). If a = 0.2, find the optimal consumption bundle of coal and gas. Does the coal rationing constraint influence consumer's choice and utility, and if so, how much? b. a. If a = 0.8, find the optimal consumption bundle. Does coal rationing constraint influence consumer's choice and utility, and if so, how much?