Concept explainers
Explanation of Solution
Formulation of LP:
Let,
The objective of the problem is to minimize the office’s weekly labour costs.
Objective function:
Minimize,
Explanation:
A full time employees work for
Constraints:
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Chapter 3 Solutions
Operations Research : Applications and Algorithms
- A furniture factory makes wooden tables, chairs, and armoires. Each piece of furniture requires three operations: cutting the wood, assembling, and finishing. Each operation requires the number of hours given below. One table requires 0.5 hours of cutting, 0.5 hours of assembling and 1 hour of finishing. One chair requires correspondingly 1, 1.5, 1.5 hours. Finally, one armoir requires 1, 1, and 2 hours. The workers in the factory can provide 300 hours of cutting, 400 hours of assembling, and 590 hours of finishing each work week. Mark only correct statements. a. For any choice of labor resources in each operation, there are different possibilities in producing tables. Ob. It is possible to use the labor resources full if finishing is reduced to 500 hours. Oc. It is impossible to use the labor resources full. O d. For any choice of labor resources in each operation, there are different possibilities in producing chairs. Oe. It is possible to use the labor resources full if cutting…arrow_forwardA company manufactures three products 1, 2, and 3. Each product requires production time in three departments as shown below: PRODUCT DEPARTMENT 1 DEPARTMENT 2 DEPARTMENT 3 1 3 hr/unit 2 hr/unit 1 hr/unit 2 4 hr/unit 1 hr/unit 3 hr/unit 3 2 hr/unit 2 hr/unit 3 hr/unit There are 500, 400, and 300 hours of production time available in the three departments, respectively. If products 1, 2, and 3 contribute $3, $4, and $2.5 per unit to profit, answer the following questions: (You may attach your solution or write in the box) a) Define the decision variables (2 marks). b) Write all constraints (3 marks). c) Write the objective function (define whether it is a maximization or minimization) (1.5 marks)arrow_forwardQ2. Consider the following case study: "Springfield University offers a number of courses. A course contains a number of units. Students enrol and elect a set of units every semester. Students are allowed to enrol in a maximum of 5 units in any given semester. They can only be enrolled into a single course at any given point in time. However over a student's lifetime, they may undertake a number of different courses. Each unit has a set fee that is set at the start of the semester. This fee is to be paid up-front in full by the students once enrolled. Some units have pre-requisite unit requirements. Some units have co-requisite unit requirements. To be enrolled in some courses, you must have completed a certain course (e.g. to enrol into a Postgraduate course, you must have an Undergraduate degree)." Noun (bold)/verb (underline) analysis on the case study is marked for you to identify candidate classes, attributes, operations. Now, draw a Specification level Class Diagram for the case…arrow_forward
- It has been observed by management that some faculty members at theuniversity demonstrate a lackadaisical attitude toward teaching. They seldom go to class yet at the end of each month they receive full salary. Management has decided that GHs 200, 300, 400, and 500 will be deducted from a faculty’s salary if he/she offends once, twice, third time and forth time respectively in a month. This means that if a faculty member offends once in a month GHs200 will be deducted, if a faculty member offends twice in a month, GHs 500 (i.e. 200+300) will be deducted, if a faculty member offends three times in a month GHs 900 (i.e. 200+300+400), will be deducted and if a faculty member offends four times in a month GHs 1,400 (i.e. 200+300+400+500). Assuming all faculty members are on a flat salary rate of GHs 2000.a. Write a program to request for the names of four faculty members and number times he/she has absented him/herself from class in a month.One of them should have absented him/herself…arrow_forwardA farmer in Georgia has a 100-acre farm on which to plant watermelons and cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day and must be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day and must be prepared for planting with 15 pounds of fertilizer. The farmer estimates that it will take 2 hours of labor to harvest each acre planted with watermelons and 2.5 hours to harvest each acre planted with cantaloupes. He believes that watermelons will sell for about $3 each, and cantaloupes will sell for about $1 each. Every acre planted with watermelons is expected to yield 90 salable units. Every acre planted with cantaloupes is expected to yield 300 salable units. The farmer can pump about 6,000 gallons of water per day for irrigation purposes from a shallow well. He can buy as much fertilizer as he needs at a cost of $10 per 50-pound bag. Finally, the farmer can hire laborers to…arrow_forwardThe Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to three regions-the South, the East, and the Midwest. A salesperson in the South earns $600 in profit per month for the company, a salesperson in the East earns $540, and a salesperson in the Midwest earns $375. The southern region can have a maximum assignment of five sales- people. The company has a total of $750 per day available for expenses for all 12 salespeople. A salesperson in the South has average expenses of $80 per day, a salesperson in the East has average expenses of $70 per day, and a salesperson in the Midwest has average daily expenses of $50. The company wants to determine the number of salespeople to assign to each region to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer.arrow_forward
- IP Applications 4 Employment for Projects Formulate the following problem as integer linear programming problem. A company hires employees from a pool of 80 people. Employees are hired on a day to day basis. The pool contains 25 experienced persons. An experienced person can do twice as much work as an inexperienced person in the same time. Our company has n projects for which it has to recruit people. For the upcoming T days employees have to be divided over the projects. For project i (i = 1; :::; n) is w, the amount of required work on day t (t = 1; :::; T); an inexperienced employee can perform one unit of work per day. If an employee is hired on a certain day, he/she works on the same project all day. The cost for hiring a normal employee are c, per day and the cost for hiring an experienced employee are c, per day. Finally, for every day the minimal number of experienced employees that has to work on project i equals u,. The company wants to minimize the cost of hiring employees.…arrow_forwardA school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 9 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? Your answer is:arrow_forwardQUESTION 15 Al Watan supermarket has hire-purchases scheme for locals and expats. The customers will get the credit facility if they satisfy any of the following conditions: 1. The customer must hold the present job for more than 5 years and reside in the same place at least for 3 years. In this case, the customer will get credit upto rupees 300 omr. 2. The monthly salary of the customer must exceed 1000 omr and must hold the present job for more than 5 years. In this case credit will be given upto rupees 500 omr. 3. The monthly salary must exceed 1000 omr and reside at the same place at least for 3 years. In this case credit will be given upto 500 omr. 4. In the case, the customer's monthly salary exceeds 1000 omr, holds the present job for more than 5 years and also reside in the same place at least for the 3 years, the credit facility will be upto 1000 omr 5. The credit facility is rejected for all other customers. Prepare a Decision Table for this hire- purchase scheme. Attach File…arrow_forward
- QUESTION 15 Al Watan supermarket has hire-purchases scheme for locals and expats. The customers will get the credit facility if they satisfy any of the following conditions: 1. The customer must hold the present job for more than 5 years and reside in the same place at least for 3 years. In this case, the customer will get credit upto rupees 300 omr. 2. The monthly salary of the customer must exceed 1000 omr and must hold the present job for more than 5 years. In this case credit will be given upto rupees 500 omr. 3. The monthly salary must exceed 1000 omr and reside at the same place at least for 3 years. In this case credit will be given upto 500 omr. 4. In the case, the customer's monthly salary exceeds 1000 omr, holds the present job for more than 5 years and also reside in the same place at least for the 3 years, the credit facility will be upto 1000 omr 5. The credit facility is rejected for all other customers. Prepare a Decision Table for this hire- purchase scheme.arrow_forward4 - If an employee is paid hourly, he is paid a fixed amount for every hour of work. So, if he gets paid $15.00 an hour, and he works eight hours his gross pay is $120.00. An hourly employee’s gross pay must be calculated on a weekly basis because of a Rule called overtime, the federal government’s Fair Labor Standards Act states that for overtime an employee must receive overtime pay for hours worked over 40 in a work week at a rate not less than 1.5 times regular rates of pay. Write a python program that ask for the hourly pay rate and the number of hours worked in a week by the employee and calculate it’s pay accordingly. If the employee worked overtime, he should be paid 1.5 times regular rates of pay for every exceeding hour. Don't use built-in methodsarrow_forwardan Administrator in a hospital who is charged to propose schedules between 30 doctors to share three surgery rooms in the hospital. The three rooms are available for booking from 8 a.m. to 4 p.m. every working day (Sunday to Thursday). The hospital policies state that each doctor should do at least one surgery(a week), Brain surgery is available every Monday and Wednesday, six consultant doctors work only during morning shift (8-12). In addition, six doctors are junior doctors and should join any senior doctors during the surgery, however, they cannot use room 3 as it is small. Furthermore, some rooms have special equipment’s required for surgeries e.g., x-ray device at room 1 and online streaming for online consultation at room 2. Solve by building a Backtracking algorithm solution with minimum empty slots. *Sample Input/Output of Smart Surgery Scheduling:* Welcome to Smart Surgery Scheduling! Please enter the names of consultants. S.T., H.D., Please enter the names of the senior…arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole