A company is in the process of releasing a compact cassette with 8 songs on it.

Question

A company is in the process of releasing a compact cassette with 8 songs on it. The length of tape required for each song is given in the table below. The tape has 2 sides, A and B. Songs will be placed on both A and B. Splitting songs across both sides is undesirable. For instance, if the company puts all songs on Side A and leaves Side B blank, they would need 326 cm of tape. But if they put the first 6 songs on Side A, and songs 7 and 8 on Side B, then they would only need 256 cm of tape Formulate a mathematical model and solve it to assign songs to each side of the tape so that the total length of the tape is minimized Table 1: Tape length for songs Length (in cm) Song My Mobile Home Honky Tonkin' Truck Won't Crank You Can Tell by the Way I Use My Chalk Hallway & Quaker Oats Polka Rocks Ballad Salad Metal Pedal 57 62 33 21 39 42 28

Explanation / Answer

Let songs be denoted as 1,2,3,4,5,6,7,8 and L1.L2......L8 denote length of tape required for those songs respectively

Now total length = 326 cm

obviously if this is split into two parts A and B then ideal length on each side = 326/2 = 163 cm

SO L1+L2+L3+.......+L8 =326

Then Sum of lenghts of any one part => 163 Cm

If we can find a combination of songs such that their lengths = 163 cm then that would be the ideal split as length of any one side can not be less than 163 cm and by identifying a combination of 163 cm the rests of the songs will also be of 163 cm. ( 163 is half of 326 i.e. full length tape)

So We use summation of Lenghts beginning from highest to lowest to find the combination that sums to 163

The desired combination is songs 1,2,3 on one side and 4,5,6,7,8, on other side

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.