A firm produces TVs and ovens with a joint cost function that takes the form: C(x,y) = 3x^2 + 2y^2 + 2xy where x and y are the firm's output of TVs and ovens respectively. Suppose the cost function is subject to the constraint on the total output of the firm in the form 2x + y = 35. a) Find the optimum values x and that minimize the firm's total cost. b) Check your answer in (a) by using the bordered Hessian matrix. c) Determine the optimum value of the Lagrange multiblier À. Interpret your answer.

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