8) Mark derives utility from watching movies and from playing computer games according to the utility function U(c,m)=6c1/3m1/2, where c is the number of hours he plays games and m is the number of hours he watches movies. He has 15 hours per day to divide between these two activities. a) Write down Mark's constrained utility maximization problem and his Lagrangian function. Derive the first order conditions and find the candidate solution (c,m). b) Compute the determinant of the bordered Hessian and evaluate it at the point A (c,m)=(271,41). Note that point A may be different from the stationary point (c,m) you found in part a). (This is so that mistakes in solving for (c,m) do not automatically carry over to this part.) c) Using the bordered Hessian, check whether the point (c,m) satisfies the second-order conditions for a constrained local maximum of this optimization