Consider a person who has to decide how spend their weekend. The person would like to `consume' leisure, but would also like to consume goods over the weekend, which would require them to work.
They have access to a job that pays by the hour and where they can choose to work as many hours as they wish. They are paid the same irrespective of whether they work on Saturday of Sunday.
Unfortunately, they also have a homework assignment to complete over the weekend, which will take them exactly four hours in total and must be done. Completing homework has no eect on the person's well-being.
Assuming that are regarded as the same thing irrespective of whether they occur on Saturday or Sunday, set out the maximization problem and derive the rst order conditions for an optimal solution. Describe each part of your model and the outcome carefully. You may assume that there is only a single consumption good with a price of $1.