Mathematical Economics

Q 1: Answer the following questions: 1) Maximize utility U = 2XY subject to a budget constraint equal to 3X + 4Y = 90 by (a) finding the critical values X, Y and A (b) using the bordered Hessian [#| to test the second-order condition. ii) Maximize utility U = XY + X subject to a budget constraint equal to 6X + 2Y = 110 by (a) finding the critical values X, F and I (b) using the bordered Hessian [H| to test the second-order condition. lil) Minimize a firm's total costs C = 45X + 90XY + 90Y? when the firm has to meet a production quota equal to 2X + 3Y = 60 by (a) finding the critical values X, F and J (b) using the bordered Hessian |#| to test the second-order condition. iv) Minimize a firm's total costs C = 3X' + 5XY + 6Y? when the firm has to meet a production quota equal to 5X + 7Y = 732 by (a) finding the critical values X, Y and X (b) using the bordered Hessian [HI to test the second-order condition. v) Maximize utility U = *05x03 subject to a budget constraint equal to 10X + 3Y = 140 by (a) finding the critical values X, F and I (b) using the bordered Hessian |#| to test the second-order condition