Please help me with last four questions, you do not need to answer the first three if you do not want to

Consider a consumer whose preferences over consumption bundles of non-negative amounts of each of two distinct commodities can be represented by a utility function of the form U (q1, 92) = q192 + 2q1 + 5q2. where q1 is the quantity of commodity one and q2 is the quantity of commodity two. Suppose that this consumer is a price taker in both markets, faces a price vector (P1, p2. ) E Ray, and is endowed with a monetary income of y > 0. You may assume that the budget constraint binds and any required constraint qualification conditions and second- order conditions for a maximum are satisfied by any solution to this consumer's budget- constrained utility maximisation problem.What is this consumer's budget-constrained utility maximisation problem? (1 mark.) What is the Lagrangean function for this consumer's budget-constrained utility maximisation problem? (1 mark.) What are the first-order conditions for this consumer's budget-constrained utility maximisation problem? (6 marks.) Find the uncompensated demand functions (or correspondences) for this consumer. Be sure to show all of your working. (Uncompensated demands are also known as Marshallian demands, or Walrasian demands, or ordinary demands.) (11 marks.) What is the point income elasticity of demand for each of the commodities? (2 marks.) What is the point own-price elasticity of demand for each of the two commodities? (2 marks.) What is the point cross-price elasticity of demand for each of the two commodities? (2 marks.)