# Question : The utility you derive from exercise (X) and watching movies

(M) is described by the function: ( , ) = 100 − e-2x −e-M .Currently you have four hours each day that you can devote either to watching movies or exercising ( + = 4).

a) Set up the Lagrangian function to maximize utility.

b) Find the optimal amount of time spent at each activity.

c) Is the second-order sufficient condition for maximum satisfied?

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