Question 6,7,9

docx

School

Florida International University *

*We aren’t endorsed by this school

Course

6357

Subject

Industrial Engineering

Date

Dec 6, 2023

Type

docx

Pages

Uploaded by DeaconElkMaster927

Question 6: Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 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 Winery, 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 project time. 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, $22 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. If an amount is zero, enter “0”. If the constant is "1" it must be entered in the box. For negative numbers use a minus sign (Example: enter -100). Let L = number of hours assigned to Lisa D = number of hours assigned to David S = number of hours assigned to Sarah Min $ ( ? ) L + $ (? ) D + $ (? ) S s.t. (? ) L + (? ) D + (? ) S ≥ (? ) Minimum Lisa (? ) L + (? ) D + (? ) S ≥ (? ) Minimum Sarah (? ) L + (? ) D + (? ) S ≤ (? ) Maximum Lisa (? ) L + (? ) D + (? ) S ≤ (? ) Maximum Sarah (? ) L + (? ) D + (? ) S = (? ) Total Time L , D , S ≥ 0 (b) How many hours should be assigned to each graphic designer? Hours Assigned Lisa (? ) David (? ) Sarah (? ) What is the total cost? If required, round your answer to a whole dollar amount. $(? )

(c) Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain. If an amount is zero, enter “0”. We know that the shadow price for this constraint is (? ) , since the constraint is - Select your answer -binding, not binding. Therefore, additional hours for Lisa will - Select your answer -change, not change (d) If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? - Select your answer -Yes, No Explain. There - Select your answer -is a, is no lower limit on the right-hand-side range, so the optimal solution - Select your answer -will, will not. Question 7: The Silver Star Bicycle Company will manufacture both men's and women's models for its Easy-Pedal bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men's and 125 women's models to be shipped during the first month and 200 men's and 150 women's models to be shipped during the second month. Additional data are shown: Labor Requirements (hours) Production Model Costs Manufacturing Assembly Current Inventory Men's $120 2.0 1.5 20 Women's $90 1.6 1.0 30 Last month, the company used a total of 1,000 hours of labor. The company's labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 31 units of each model in inventory at the end of the two months. (Hint: Define variables for production and inventory held in each period for each product. Then use a constraint to define the relationship between these: inventory from end of previous period + produced this period - demand this period = inventory at end of this period.) (a) Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements. What inventories will be maintained and what are the monthly labor requirements? If required, round your answers to nearest whole number. If your answer is zero, enter “0”. Production schedule: The optimal solution is as follows Production Schedule Men's Model Women's Model Month 1 ( ) ( ) Month 2 ( ) ( ) Total Cost = $( ) Inventory Schedule Men's Women's

Month 1 ( ) ( ) Month 2 ( ) ( ) If required, round your answer to two decimal places. Labor Levels Previous month ( ) hours Month 1 ( ) hours Month 2 ( ) hours (b) If the company changed the constraints so that monthly labor increases and decreases could not exceed 50 hours, what would happen to the production schedule? If required, round your answers to nearest whole number. Production schedule: The revised optimal solution is as follows Production Men's Model Women's Model Month 1 ( ) ( ) Month 2 ( ) ( ) Total Cost = $( ) How much will the cost increase? $( ) What would you recommend? The input in the box below will not be graded, but may be reviewed and considered by your instructor. Question 9: The Clark County Sheriff’s Department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m. An officer beginning a shift at one of these times works for the next 8 hours. During normal weekday operations, the number of officers needed varies depending on the time of day. The department staffing guidelines require the following minimum number of officers on duty: Time of Day Minimum No. of Officers on Duty 8:00 a.m.–noon 5 Noon–4:00 p.m. 6 4:00 p.m.–8:00 p.m. 8 8:00 p.m.–midnight 7

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Midnight–4:00 a.m. 4 4:00 a.m.–8:00 a.m. 6 Determine the number of police officers that should be scheduled to begin the 8-hour shifts at each of the six times to minimize the total number of officers required. If your answer is zero, enter “0”. Starting Time Officers Starting 8:00 a.m. ( ) Noon ( ) 4:00 p.m. ( ) 8:00 p.m. ( ) Midnight ( ) 4:00 a.m. ( )

Question 6,7,9

Related Documents