In Problem 10, suppose that the nature of the melodies dictates that songs 3 and 4 cannot be recorded on the same side. Formulate the problem as an ILP. Would it be possible to use a 25-minute tape (each side) to record the eight songs? If not, use ILP to determine the minimum tape capacity needed to make the recording.

In problem

The Record-a-Song Company has contracted with a rising star to record eight songs. The durations of the different songs are 8,3,5,5,9,6,7, and 12 minutes, respectively. Recorda- Song uses a two-sided cassette tape for the recording. Each side has a capacity of 30 minutes. The company would like to distribute the songs between the two sides such that the length of the songs on each side is about the same. Formulate the problem as an ILP, and find the optimum solution.