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Question : There a single mother with two children deciding how many

There is a single mother with two children deciding how many hours to work in a month. She could work a maximum of 160 hours in the month, so in this problem we'll say the most leisure, L, she could have would be 160 hours. If she works, she receives $6 per hour of work. If she works, all of her earnings are used for consumption, C. She has a utility function that describes her preferences as: U = 3 ln C + 5 ln L. Her budget constraint in this case is 6*(160 - L) = C. Suppose the government introduces a welfare program that gives a $120 benefit that has a benefit reduction rate of 20%. Solve for her new optimal choice of labor supply.