A consumer has the following utility function U(x1,x2)=(x1 +3)(x2+4) Prices of the two goods x1 and x2 respectively are p1 and p2 and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m is high enough so that both goods are consumed in strictly positive amount in equilibrium. (a) (3 marks) Solve the consumer's optimization problem and express the demand for the two goods in terms of prices and income.