1. Industrial Designs has been awarded a contract to design a label for a new wineproducedbyLakeViewWinery.Thecompanyestimatesthat 150 hourswill berequired to complete the project.The firm's three graphics designers available forassignment to this project are Lisa, a senior designer and team leader; David, a seniordesigner;andSarah,ajuniordesigner.BecauseLisahasworkedonseveralprojectsforLakeViewWinery,managementspecified that Lisamust be assignedat least40% of the total number of hours assigned to the two senior designers.To providelabel-designing experience for Sarah, Sarah must be assigned at least 15% of the totalproject time. However, the number of hours assigned to Sarah must not exceed 25% ofthetotalnumberofhoursassignedtothetwoseniordesigners.Duetootherproject

commitments, Lisa has a maximum of 50 hours available to work on this project.Hourlywageratesare$30forLisa,$25forDavid,and$18forSarah.

1. Formulate a linear program that can be used to determine the number ofhours each graphic designer should be assigned to the project in order to minimizetotalcost.
2. Howmanyhoursshouldeachgraphicdesignerbeassignedtotheproject?Whatisthetotalcost?
3. Suppose Lisa could be assigned more than 50 hours. What effect would thishaveontheoptimalsolution.Explain.
4. If Sarah were not required to work a minimum number of hours on thisproject,wouldtheoptimalsolutionchange?Explain.