3. (25 points) A consumer's preferences between goods 1 and 2 are represented by the utility function u(x1, x2) = x1x2, where x1 denotes the quantity consumed of good 1 and x2 denotes the quantity consumed of good 2. Suppose that this consumer's income is $16 and the prices are given by p1 = $1 for good 1 and p2 = $2 for good 2. Find the optimal consumption bundle for this consumer. Represent his optimal choice with a graph.