11. A consumer gets utility not only out of the two goods that he consumes, but also from the income he has left over after consumption. Suppose the consumer's utility function is given by u(c1, c2, m) where c; denotes the quantity consumed of commodity i, and m > 0 is the left-over income. Suppose further that u is strictly increasing in each of the three arguments. Assuming that the consumer has an income of I > 0, that the price of commodity i is Pi > 0, and that all the usual nonnegativity constraints hold, answer the following questions: (a) Set up the consumer's utility maximization problem, and describe the Kuhn- Tucker first-order conditions. (b) Explain under what further assumptions, if any, these conditions are also sufficient for a maximum