Distance to School с Sector School in Sector School in Sector School in Sector B Number of Students E А 504 ABCDE 8 6 700 4 12 500 0 7 100 7 2 5 800 12 7 0 400 Total 2,500 Each high school has a capacity of 900 students. You have been asked to develop a linear programming model so as to minimize the total number of student miles traveled by bus. Decision variable X,,: Number of students living in sector i traveling to school located in sector j. The number of decision variables for the model = 15. a) The objective function, for the LP model = Minimize Z = 5X AB +8XAC +6XAE + 5XAB Subject to: ^BB ^BC ^BE 4XCB +0XCC +7XCE 7XDB + 7X DB + 2X DC +5X DE + 12 XEB+7XEC+0XEE X AB+X AC +X AE = 700 ХАВ XBB+X BC +X BE = 500 XCB+X CC+X CE = 100 A B number of students in sector number of students in sector number of students in sector C number of students in sector X DB +X DC +X DE == 800 D number of students in sector XEB +XEC +XEE = 400 E ХАВ + XBB + XCB + Хас XAE XCE + X CE + X DE XAC + XBC + XCC + XDC + X EC ≤900 + X BE XDB +XEB ≤900 school B capacity school C capacity + XEE ≤900 school E capacity non negativity condition For all X >

Distance to School с Sector School in Sector School in Sector School in Sector B Number of Students E А 504 ABCDE 8 6 700 4 12 500 0 7 100 7 2 5 800 12 7 0 400 Total 2,500 Each high school has a capacity of 900 students. You have been asked to develop a linear programming model so as to minimize the total number of student miles traveled by bus. Decision variable X,,: Number of students living in sector i traveling to school located in sector j. The number of decision variables for the model = 15. a) The objective function, for the LP model = Minimize Z = 5X AB +8XAC +6XAE + 5XAB Subject to: ^BB ^BC ^BE 4XCB +0XCC +7XCE 7XDB + 7X DB + 2X DC +5X DE + 12 XEB+7XEC+0XEE X AB+X AC +X AE = 700 ХАВ XBB+X BC +X BE = 500 XCB+X CC+X CE = 100 A B number of students in sector number of students in sector number of students in sector C number of students in sector X DB +X DC +X DE == 800 D number of students in sector XEB +XEC +XEE = 400 E ХАВ + XBB + XCB + Хас XAE XCE + X CE + X DE XAC + XBC + XCC + XDC + X EC ≤900 + X BE XDB +XEB ≤900 school B capacity school C capacity + XEE ≤900 school E capacity non negativity condition For all X >

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.5: Shortest Path Models

Problem 31P

See similar textbooks

Similar questions

E-5 Boston Executive, Inc., produces executive limousines and currently manufactures the mini-bar inset at these costs: (refer the attached image) The company received an offer from Elite Mini-Bars to produce the insets for $2,100 per unit and supply 1,000 mini-bars for the coming year’s estimated production. If the company accepts this offer and shuts down production of this part of the business, production workers and supervisors will be reassigned to other areas. Assume that for the short-term decision-making process demonstrated in this problem, the company’s total labor costs (direct labor and supervisor salaries) will remain the same if the bar inserts are purchased. The specialized equipment cannot be used and has no market value. However, the space occupied by the mini-bar production can be used by a different production group that will lease it for $55,000 per year. Should the company make or buy the mini-bar insert?
2. A company has plants at locations A, B and C with the daily capacity to produce chemicals to a maximum of 3000 kg, 1000 kg and 2000 kg respectively. The cost of production (per kg) are P800, P900 and P750 respectively. Customer's requirement of chemicals per day is as follows: Customer Chemical Required Price offered 2000 200 2 1000 215 3 2500 225 1000 200 Transportation cost per kg from plant locations to customer's place is given in table. Customer 2 3 A 5 7 10 12 Plant B 3 4 2 с 3 Find the transportation schedule that minimizes the total transportation cost.
(A) Determine the total number of future trips generated in all zone? This table shows Number of currant Household and currant trips Zone A Zone B Zone C No. of No. of No. of person/Household = person/Household = person/Household = Auto/ Household 1 2-3 >3 No. of No. of No. of No. of No. of No. of Н.Н trips Н.Н trips Н.Н trips 1100 220 1500 600 1800 1080 1 950 380 1200 600 120 90 >1 80 100 200 300 50 80 This table shows Number of future Household Zone A Zone B Zone CTH No. of No. of No. of Auto/ Household person/Household = person/Household = person/Household 1 2-3 >3 3000 5000 6000 1 1500 4000 800 >1 300 700 200
a. A farmers' cooperative association plans to build a new sugar mill in Georgetown. The primary objective of the mill is to provide the farmers with a place to take their crop for processing that will reduce their transportation costs. The members of the co-op believe that the center-of-gravity method is appropriate for this objective. While there are over 200 sugar cane farms in the region, they are tightly clustered around six villages. Using the data below, use the center-of-gravity method to calculate the coordinates of the best location for this mill. All mileage references use Browns Town as (0,0). Village Barney Valley Blue Pasture Congo Valley Bower Rabacca Salem Miles East of Miles North of Sugar Cane Browns Town Browns Town 90 140 20 50 100 10 10 60 70 20 80 120 tonnage 240,000 320,000 450,000 120,000 60,000 140,000
Gongjin Hotel is a budget hotel in the province of Gyeongsan. Due to the COVID-19 pandemic, the hotel wanted to convert the hotel to a facility for OFWs that were returning to the country because of the protocols mandated by the government where they need to be quarantined for 3-7 days before returning to their cities. Furthermore, the hotel is expected to be fully booked because they are the only hotel that would offer this service. Being the Executive Housekeeper, how will you encourage the general manager to convert the hotel? What protocols would you be implementing for the hotel as well for the housekeeping employees for them to be allowed to convert to the hotel? Give at least five (5) recommendations and support your answers with related literature.
Please show solution and formula used. Assuming the total number of students studying in the top four universities in the Philippines is approximately 158,000. And the distribution is as follows: University of the Philippines (UP) - 40% of the total number Ateneo de Manila University (ADMU) - 23,700 De La Salle University (DLSU) - 25% of the total number University of Santo Tomas - 20% of the total number And only the following number of students owns a tablet computer: 20% of UP students 85% of ADMU students 90% of DLSU students 85% of UST students What is the total market penetration of tablet computers among the students of the top four universities? What is the total market size of tablet computers in the top four universities?
5 نقاط Find the Optimal Value of the Objective Function for Linear Programming Problem ( Choose the *: appropriate method) min Z = 6 x + 2 y + 15.8 s.t: -x+ 2 y 20 х,у 20 x= 0 , y=2, Z= 19.8 O x= 0.3 , y=2, Z= 20.4 O X= 0.5, y=2, Z= 18.9 x= 0.9 , y=0.3 , Z= 21.8 O O أخری:
Maximize 8x + 9y Subject to -- x + 2 y 0 a) Solve using simplex method
Civil engineering consulting fi rms that provide ser-vices to outlying communities are vulnerable to a number of factors that affect the fi nancial conditionof the communities, such as bond issues and real estate developments. A small consulting fi rm en-tered into a fi xed-price contract with a large devel-oper, resulting in a stable income of $260,000 per year in years 1 through 3. At the end of that time, a mild recession slowed the development, so the par-ties signed another contract for $190,000 per year for 2 more years. Determine the present worth of thetwo contracts at an interest rate of 10% per year.
The Dynaco Manufacturing Company produces a product in a process consisting of operations of five machines. The probability distribution of the number of machines that will break down in a week follows: Machine Breakdowns Probability per Week 0.1 0.2 2 0.1 0.25 0.3 0.05 a. Simulate the machine breakdowns per week for 20 weeks. 4. b. Compute the average number of machines that will break down per weck.
3. Figure 1 Daily Subway and Bus Use in Five Major Cities 0.75 0.5 0.25 Subway OBus London Tokyo Singapore Hong Kong Figure 2 Subway vs. Bus Ridership, New York City OBus Subway 1970 1980 1990 2000 2010 Information in figure I suggests that public transportation users in London Information in Figure I supports the author's point that buses are growing in popularity as a means of urban transport by indicating that A) take subways and buses at similar rates. B) are unusually reliant on buses. C) take at least one subway trip daily. D) take subways at about the same rate as people A) many people around the world take at least one bus trip every day. B) bus ridership surpasses subway ridership in some major cities. C) people in Tokyo make far more trips by bus daily than they do trips by subway. D) the number of bus trips taken by people in major cities has substantially increased. in New York. 2 Which of the following statements about bus use in New York City is best supported by…
Problem 1. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 20 salespeople given the information below. Shift Morning Midday Afternoon Evening The average number of customers 95 305 435 515 Determine the apportionment using Hamilton’s Method Jefferson’s Method Webster Method Huntington-Hill Method