Consider an individual with preferences given by U$($L$,$C$)=$LC$.$ Assume the wage rate is $$4$ per hour and the maximum time available per month is $400$ hours. Also assume initially that the person has nonlabor income of $$200.$ Suppose the individual incurs a fixed monetary cost of $$100$ per month associated with working and a fixed time cost of $30$ hours per month. a$.$ Find the optimal amount of leisure and work that can be attained and the level of utility achieved. Verify that the level of utility is greater than that attained by not working at all. b$.$ Suppose both the monetary and time costs of working are eliminated by work from home $($WFH$).$ Find the optimal number of leisure and work hours and the level of utility achieved.