1: Answer the following questions: i) Maximize utility = 2 subject to a budget constraint equal to 3 + 4 = 90 by (a) finding the critical values , and (b) using the bordered Hessian || to test the second-order condition. ii) Maximize utility = + subject to a budget constraint equal to 6 + 2 = 110 by (a) finding the critical values , and (b) using the bordered Hessian || to test the second-order condition. iii) Minimize a firm's total costs = 45 2 + 90 + 90 2 when the firm has to meet a production quota equal to 2 + 3 = 60 by (a) finding the critical values , and (b) using the bordered Hessian || to test the second-order condition. iv) Minimize a firm's total costs = 3 2 + 5 + 6 2 when the firm has to meet a production quota equal to 5 + 7 = 732 by (a) finding the critical values , and (b) using the bordered Hessian || to test the second-order condition. v) Maximize utility = 0.5 0.3 subject to a budget constraint equal to 10 + 3 = 140 by (a) finding the critical values , and (b) using the bordered Hessian || to test the second-order condition