Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Expert Solution & Answer
Chapter 5.1, Problem 2P
Explanation of Solution
Optimal solution
- The optimal solution to the linear problem occurs when the two constraints are binding.
- Hence the optimal solution is the solution to
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The Pee Tool Shop has four heavy presses it uses to stamp out prefabricated metal covers and housings
for electronic consumer products. All four presses operate differently and are of different sizes.
Currently the firm has a contract to produce three products. The contract calls for 400 units of product
1; 570 units of product 2; and 320 units of product 3. The time (in minutes) required for each product
to be produced on each machine is as follows: SOLVE THE MODEL BY USING MS EXCEL
La Taqueria has five food trucks parked permanently around the city. Each week, cases of burritos must be delivered from El Mercado to the five trucks. The table shows the travel time in minutes between the locations as well as from El Mercado (location o).
Assume that only one delivery truck is available and has a capacity of 50 cases.
Delivery Time
il 01
0
6
1
2
3
23 4 5
27 26 21 47
21
Cases
8 13 15 15
20
27 35 34
33
11
22
O c0-1-2-0, 0-3-0, 0-4-5-0
O d. 0-1-2-0, 0-3-4-0, 0-5-0
12
38
42
5
What is the most economical routing for the delivery truck?
O a. 0-1-2-0, 0-3-0, 0-4-0, 0-5-0
O b. 0-2-3-0, 0-1-0, 0-4-0, 0-5-0
ACE Hardware wants to develop a daily schedule for its employees in one of its stores in Omaha. Currently,this store has five employees and the store is opened from 12pm to 9pm. The store must always have at leasttwo people on hand. Each employee must work at least four hours and no more than eight hours per day.Employee #1 goes to school and cannot start before 4pm while all other employees can work at any time.Furthermore, employee #1 earns $10 per hour while all other employees earn $12 per hour. Because all fiveemployees live so close to the store, you must assume that they do not need to work consecutive hours.a) Formulate an optimization model for this problem.b) Solve the optimization model using either the Microsoft Excel Solver or the IBM ILOG CPLEXOptimization Studio.
Chapter 5 Solutions
Operations Research : Applications and Algorithms
Ch. 5.1 - Prob. 1PCh. 5.1 - Prob. 2PCh. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Prob. 5PCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5P
Ch. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Prob. 11PCh. 5 - Prob. 1RPCh. 5 - Prob. 2RPCh. 5 - Prob. 3RPCh. 5 - Prob. 4RPCh. 5 - Prob. 6RPCh. 5 - Prob. 7RPCh. 5 - Prob. 8RPCh. 5 - Prob. 9RPCh. 5 - Prob. 10RPCh. 5 - Prob. 11RPCh. 5 - Prob. 12RPCh. 5 - Prob. 13RPCh. 5 - Prob. 14RPCh. 5 - Prob. 15RPCh. 5 - Prob. 16RP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- The Callaghan family owns 410 acres of farmland in Co. Cork on which they grow wheat and oats. Each acre of wheat costs €105 to plant, cultivate, and harvest; each acre of oats costs €210. The Bradleys have a budget of €52,500 for next year. The government limits the number of acres of oats that can be planted to 100. The profit from each acre of wheat is €300; the profit from each acre of oats is €520. The Callaghans want to know how many acres of each crop to plant in order to maximize their profit. ii. Formulate a linear programming model for this problem.arrow_forwardA company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled. It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Use Solver to maximize the company’s profitarrow_forwardSaudi Aramco uses three containers to deliver gasoline and diesel fuels to Hafr Albatin once a week. Each container has 3 spaces, with volumes: 350, 550, and 670 liters. The second container cannot carry gasoline fuel in any of its spaces. The weekly demand for gasoline and diesel, is 2600, and 2100 liters respectively. Private companies will transport any quantity that Saudi Aramco containers cannot deliver. Private companies charge 0.45 riyal/liter of gasoline and 0.25 riyal/liter of diesel. Construct an integer program that Saudi Aramco could use to load its containers so that the total cost of private shipping is minimized. Define the variables clearly. Write the constraints in full, do not use E sign. Do not use j, instead use j = 1, ., 10.arrow_forward
- Six months before its annual convention, the AmericanMedical Association must determine how many rooms toreserve. At this time, the AMA can reserve rooms at a costof $50 per room. The AMA must pay the $50 room costeven if the room is not occupied. The AMA believes that thenumber of doctors attending the convention will be normallydistributed, with a mean of 5,000 and a standard deviationof 1,000. If the number of people attending the conventionexceeds the number of rooms reserved, extra rooms must bereserved at a cost of $80 per room. Use simulation todetermine the number of rooms that should be reserved tominimize the expected cost to the AMA.arrow_forward3. National Disc Corp. produces the discs used in producing Xbox and PlayStation discs. Their local plant runs 24 hours a day, 7 days a week. In a given day, there are requirements for the total number of employees that must be at the plant. These are given below. Employees Needed Hours 12am - 4am 4am - 8am 8am-12pm 12pm - 4pm 4pm - 8pm 8pm-12am 8 10 16 21 18 12 Employees can either work 8-hour or 12-hour shifts, starting at the times stated above (12- hour shifts can start only at 12 am/pm or 8 am/pm). Those working 8-hour shifts cost the company $40 per hour in benefits, and those working 12-hour shifts cost the company $60 per hour. Develop a linear program that can be used to determine how National should staff the local plant so as to minimize labor costs (you do not need to solve the model). Be sure to clearly identify your variables.arrow_forwardA company's three factories produce 1,000 refrigerators per week. Plant A produces 350 refrigerators per week, while plants B and C produce 250 and 400 refrigerators per week, respectively. According to production records, 5% of the refrigerators manufactured at plant A will be defective, 3% of the refrigerators manufactured at plant B will be defective, and 7% of the refrigerators manufactured at plant C will be defective. Each refrigerator is transported to a central facility. If a defective refrigerator is discovered in the warehouse, what is the likelihood that it was manufactured at plant A? Display your workarrow_forward
- A call center has 60 employees on‐line, each of whom make one phone call every 3 min on average, and talk on average for 2 min. Each call costs 15¢. What is the total traffic in erlangs? How many circuits are required for a GoS of 1%? How much should the yearly (250 working days, 8 working hours a day) lease price be for the company to make a 50% saving in its telephone bills over the first 3 years? Assume the lease set‐up fee of $30,000 should be paid over a period of 3 years.arrow_forwardA food distribution plant for apples, oranges, bananas, and pears must get rid of extra inventory. They have advertised to all grocery stores to drop by with their cube van trucks to load up on these free products. Each truck will be loaded with the four products to a maximum of 1000 cubic feet. Each truck must be loaded with the following product distributions: 25% apples, 20% oranges, 40% bananas, and 15% pears. When all four products are loaded, the next truck can be processed. Under no circumstances should loading a truck take longer than 30 minutes. If 30 minutes is reached, loading must stop immediately, and the truck must leave. The shipping bay's operation hours are strictly enforced and will only operate between the hours of 08:00 AM to 17:00 (05:00PM). Trucks will not be served earlier than 08:00 and when 17:00 is reached operations must swiftly stop (this means it is possible to have a partially loaded truck if 17:00 is reached during the loading process). There are 10 truck…arrow_forwardIKEO is a furniture manufacturer which produces two sizes of wood blocks (type A and B) thatare used to make either a table or a chair. A table is made of a type A and a type B wood blocks,while a chair is made of a type A and two type B wood blocks (See Figure 1) A table makes RM 3 profit, and a chair makes RM 5 profit. If M number of type A and Nnumber of type B wood blocks are produced, how many tables and chairs should themanufacturer make to obtain the greatest profit?For example, let M = 12 and N = 12.By making 4 tables (4 type A and 4 type B) and 4 chairs (4 type A and 8 type B), themanufacturer gain profit as follows,Profit = (RM 3) × 4 + (RM 5) × 4 = RM 32.If the manufacturer makes 2 more tables and 1 less chair, the profit will be increased as follows,Profit = (RM 3) × 6 + (RM 5) × 3 = RM 33.Is this the greatest profit? Write a complete C++ program to help the manufacturer determine the greatest profit obtainfrom making tables and chairs with a given number of M type A and N…arrow_forward
- A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below. Bulldozer/ A B C D Site Students 1 90 75 75 80 solve it 2 35 85 55 65 yourself 3 125 95 90 105 4 45 110 95 115 How should the bulldozers be moved to the construction sites in order to minimize the total distance traveled?arrow_forwardVandelay Industries has 275 sales reps in order to sell its latex products, each to be assigned to one of four marketing teams. If the first team is to have four times as many members as the second team and the third team is to have five times as many members as the fourth team, how can the members be distributed among the teams?arrow_forwardA company uses four special tank trucks to deliver four different gasoline products to customers. Eachtank has five compartments with capacities: 500, 750, 1200, 1500, and 1750 gallons. The daily demands forthe four products are 10000, 15000, 12000, and 8000 gallons. Any quantities that cannot be delivered by thecompany’s four trucks must be subcontracted at the additional costs of 5, 12, 8, and 10 cents per gallon forproducts 1, 2, 3, and 4, respectively. The goal is to develop the optimal daily loading schedule for the fourtrucks that will minimize the additional cost of subcontracting. Formulate this problem as an integer linearprogram, and solve it (not by hand).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole