Beautiful Images has been awarded a contract to design a label for a new wine produced by Carolina Vines Winery. The company estimates that one-hundred-fifty hours will be required to complete the project. The firm’s three graphics designers available for assignment to this project are Scott, a senior designer and team leader; Brett, a senior designer; and Claudia, a junior designer. Because Scott has worked on several projects for Carolina Views Winery, management specified that Scott must be assigned at least Forty percent of the total number of hours assigned to the two senior designers. To
Beautiful Images has been awarded a contract to design a label for a new wine
produced by Carolina Vines Winery. The company estimates that one-hundred-fifty hours will be
required to complete the project. The firm’s three graphics designers available for
assignment to this project are Scott, a senior designer and team leader; Brett, a senior
designer; and Claudia, a junior designer. Because Scott has worked on several projects
for Carolina Views Winery, management specified that Scott must be assigned at least
Forty percent of the total number of hours assigned to the two senior designers. To provide
a label-designing experience for Claudia, Claudia must be assigned at least Fifteen percent of the total project time. However, the number of hours assigned to Claudia must not exceed twenty-five percent of the total number of hours assigned to the two senior designers. Due to other project commitments, Scott has a maximum of fifty hours available to work on this project.
Hourly wage rates are Thirty-dollars for Scott, twenty-five dollars for Brett, and Eighteen-dollars for Claudia.
a. Please formulate a linear program that can be used to determine the number of
hours each graphic designer should be assigned to the project in order to minimize
total cost.
b. How many hours should each graphic designer be assigned to the project?
And what is the total cost?
c. Suppose Scott could be assigned more than 50 hours. What effect would this
have on the optimal solution? Please elaborate.
d. If Claudia were not required to work a minimum number of hours on this
project, would the optimal solution change? Elaborate.
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