# Case Study – Chapter 3

Morden Shapiro

## Child Custody Negotiations

### Background

Peter and Gwen recently divorced. They have one child: Carl – 13 years old

Peter and Gwen have a collegial relationship when it come to Carl’s welfare.

Carl will live with Gwen and will visit with Peter on weekends as arranged between the parents.

Peter is a skilled draftsman. His boss, Elaine understands his situation and has given him the following degree of certainty to assist in his planning for his time with Carl.

• Peter’s hourly rate of pay for the coming year will be \$45.00 per hour
• Peter’s usual work hours will be 9 – 5 Monday – Friday, including one-hour unpaid lunch break. He can work additional hours on weekends and for those hours he will be paid at 1 ½ times his usual rate of pay. He may not work more than 150 overtime hours in the year, and no more than 5 overtime hours per day. Assume that 5 days of statutory holidays fall on a weekend day and thus those days are not available for overtime work. As per the government employment standards regulations, Peter will receive paid time off for each statutory holiday, including paid time off in lieu of the statutory holidays falling on weekends on the basis of his regular workday pay.
ASSUME: Because his employer is so busy with client work, there will always be sufficient work available for Peter whenever he wishes to work, subject to the constraints imposed by Elaine.

Peter has determined that he needs to earn at least \$83,000 in order to meet his various obligations.

### The Issue

Peter and Gwen have informally discussed the possibility that Carl would spend every weekend with Peter. Peter, Carl and Gwen would all be happy with such an arrangement. Peter is unsure if has can/should commit to such an arrangement given his need to earn at least \$83,000 annually.

### Assignment

1. In mathematical terms express Peter’s income earning potential based on the constraints noted above. Your solution should provide Peter with Yes / No answers to the following question: Can I commit to the “every weekend” time with Carl?
2. If Peter is not able to commit every weekend with Carl then, based on your solution to A, how many weekends can Peter commit to, given his constraints?

Attribution: Case study by Morden Shapiro (Ontario Tech University), published under Creative Commons Attribution-NonCommercial-ShareAlike licence (CC-BY-NC-SA)

Any modifications to this case study may affect its solvability and caution is advised.