Question

he Record-a-Song Company has contracted with a rising star to record eight songs. The sizes in MB of the different songs are 8, 10,8,7,9,6,7, and 12, respectively. Record-a- Song uses two CDs for the recording. Each CD has a capacity of 40 MB. The company would like to distribute the songs between the two CDs such that the used space on each CDs is about the same. Formulate the problem as an ILP, and find the optimum solution

Answer 1

Size 12 Decision Variables Whether to put a song on a CD or not. Variables are bina Son CD1 CD2 Objective function Maximize the number of songs put on both CDs 10 -SUM(B6:17) Constraints 12 SUM(B6:17) 13 -SUMPRODUCT (B6:16,SB$2:$i$2) 14-SUMPRODUCT(B7:17,SB$2:$I$2) 15 SUMPRODUCT B6:16,B2:12 16 SUMPRODUCT(B7:17,B2:12

Son Size 4 10 12 Decision Variables Whether to put a song on a CD or not. Variables are binary 4 Son CD1 CD2 4 Objective function Maximize the number of songs put on both CDs 10 Constraints 12

Solver Parameters Set Objective SAS10 To: O Max OMin alue Of By Changing Variable Cells: SBS6:SIS7 Subject to the Constraints: SAS12:SAS14 SCS12:SCS14 SAS15 SCS15 SBS6:SIS7binary Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Solve Close Help

Decision Variables Whether to put a song on a CD or not. Variables are binary 4 4 2 Son CD1 CD2 Objective function Maximize the number of songs put on both CD:s 10 Constraints 12 13 39 39 39 39 16