A & 4. [-/17 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Industrial Designs has...

Transcribed Image Text:

A & 4. [-/17 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Industrial Designs has been awarded a contract to design a label for a new juice mix produced by Lake View Company. The company estimates that at least 140 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total hours that ends up to be spent on the project. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.) Min s.t. Minimum Lisa Minimum Sarah Maximum Lisa Maximum Sarah Total Time L, D, 5 20 (b) How many hours should be assigned to each graphic designer? Lisa's Hours David's Hours Sarah's Hours What is the total cost (in dollars)? hours hours hours $ (c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain. Since the constraint is -Select- , additional hours for Lisa -Select- change the solution. (d) If the minimum number of work hours on the project were higher, would the optimal solution change? Explain. Since the constraint is -Select--, assigning more hours to the project -Select- change the solution. Submit Answer 13 X S mathPad Operations Functions Symbols Relations Sets Trig Greek Help A & 4. [-/17 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Industrial Designs has been awarded a contract to design a label for a new juice mix produced by Lake View Company. The company estimates that at least 140 hours will be required to complete the project. The firm's three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total hours that ends up to be spent on the project. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah. (a) Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.) Min s.t. Minimum Lisa Minimum Sarah Maximum Lisa Maximum Sarah Total Time L, D, 5 20 (b) How many hours should be assigned to each graphic designer? Lisa's Hours David's Hours Sarah's Hours What is the total cost (in dollars)? hours hours hours $ (c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain. Since the constraint is -Select- , additional hours for Lisa -Select- change the solution. (d) If the minimum number of work hours on the project were higher, would the optimal solution change? Explain. Since the constraint is -Select--, assigning more hours to the project -Select- change the solution. Submit Answer 13 X S mathPad Operations Functions Symbols Relations Sets Trig Greek Help