A consumer has preferences for two goods, it and y, expressed by the following utility function: We, 2;) = army\"- The price of x is Pm, the price of y is Pu and her budget is $'l DUB. The consumer wishes to choose the quantities in: and y that maximize her utility subject to her budget constraint. 1. Write down the consumer's budget constraint. 2. Write down the Lagrangian for this constraint optimisation problem. 3. Using the principles of constraint optimisation, find out the optimal demand function for both goods at and y. 4. Find the price elasticity of demand for good a: at the equilibrium and interpret the meaning of the elasticity