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
Question
Chapter 3, Problem 3RP
Program Plan Intro
Linear
- The linear programming(LP) is also known as linear optimization.
- Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.
- The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.
- More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
41. A machine is purchased for P 55,000. The salvage value in 20 years is P 10,000. What is the depreciation in the first three years using straight line method?
A.P 6,750
B. P6,850
C. P 6,570
D. P 6,580
A company produces two products on two machines. A unit of product 1 requires 2 hours on machine 1 and 1 hour on machine 2. For product 2, a unit requires 1 hour on machine 1 and 2 hours on machine 2. The revenues per unit of products 1 and 2 are $2 and $3, respectively. The total daily processing time available for machine 1 and 2 are 4 and 5 hours respectively. Letting and represent
the daily number of units of products 1 and 2 respectively,
(i)Construct the LP model to maximize profit.
Obtain the optimum solution graphically by determining the number of units of each product to be produced in order to maximize
the profit and at what value.
If management decides to increase the daily capacity of machine 1 from 4 hours to 5 hours, locate the new optimum point.
Compute and comment on the dual price and the feasibility range for machine 1.…
A farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50, and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and a tiller are rented. The tractor is available for 150 hours, and the tiller is available for 200 hours. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. How many acres of each crop should be planted to maximize the farmer’s profit? (Let W be the number of acres of wheat to be planted, B the number of acres of barley to be planted and P the profit) What is the objective function for the problem? Excluding the non-negative constraint, how many constraints does the problem have? What is the linear programming model of the problem? In the initial tableau, what is the leaving variable? What is the pivot element in the initial tableau? What is the optimal solution to the problem? After how many…
Chapter 3 Solutions
Operations Research : Applications and Algorithms
Ch. 3.1 - Prob. 1PCh. 3.1 - Prob. 2PCh. 3.1 - Prob. 3PCh. 3.1 - Prob. 4PCh. 3.1 - Prob. 5PCh. 3.2 - Prob. 1PCh. 3.2 - Prob. 2PCh. 3.2 - Prob. 3PCh. 3.2 - Prob. 4PCh. 3.2 - Prob. 5P
Ch. 3.2 - Prob. 6PCh. 3.3 - Prob. 1PCh. 3.3 - Prob. 2PCh. 3.3 - Prob. 3PCh. 3.3 - Prob. 4PCh. 3.3 - Prob. 5PCh. 3.3 - Prob. 6PCh. 3.3 - Prob. 7PCh. 3.3 - Prob. 8PCh. 3.3 - Prob. 9PCh. 3.3 - Prob. 10PCh. 3.4 - Prob. 1PCh. 3.4 - Prob. 2PCh. 3.4 - Prob. 3PCh. 3.4 - Prob. 4PCh. 3.5 - Prob. 1PCh. 3.5 - Prob. 2PCh. 3.5 - Prob. 3PCh. 3.5 - Prob. 4PCh. 3.5 - Prob. 5PCh. 3.5 - Prob. 6PCh. 3.5 - Prob. 7PCh. 3.6 - Prob. 1PCh. 3.6 - Prob. 2PCh. 3.6 - Prob. 3PCh. 3.6 - Prob. 4PCh. 3.6 - Prob. 5PCh. 3.7 - Prob. 1PCh. 3.8 - Prob. 1PCh. 3.8 - Prob. 2PCh. 3.8 - Prob. 3PCh. 3.8 - Prob. 4PCh. 3.8 - Prob. 5PCh. 3.8 - Prob. 6PCh. 3.8 - Prob. 7PCh. 3.8 - Prob. 8PCh. 3.8 - Prob. 9PCh. 3.8 - Prob. 10PCh. 3.8 - Prob. 11PCh. 3.8 - Prob. 12PCh. 3.8 - Prob. 13PCh. 3.8 - Prob. 14PCh. 3.9 - Prob. 1PCh. 3.9 - Prob. 2PCh. 3.9 - Prob. 3PCh. 3.9 - Prob. 4PCh. 3.9 - Prob. 5PCh. 3.9 - Prob. 6PCh. 3.9 - Prob. 7PCh. 3.9 - Prob. 8PCh. 3.9 - Prob. 9PCh. 3.9 - Prob. 10PCh. 3.9 - Prob. 11PCh. 3.9 - Prob. 12PCh. 3.9 - Prob. 13PCh. 3.9 - Prob. 14PCh. 3.10 - Prob. 1PCh. 3.10 - Prob. 2PCh. 3.10 - Prob. 3PCh. 3.10 - Prob. 4PCh. 3.10 - Prob. 5PCh. 3.10 - Prob. 6PCh. 3.10 - Prob. 7PCh. 3.10 - Prob. 8PCh. 3.10 - Prob. 9PCh. 3.11 - Prob. 1PCh. 3.11 - Show that Finco’s objective function may also be...Ch. 3.11 - Prob. 3PCh. 3.11 - Prob. 4PCh. 3.11 - Prob. 7PCh. 3.11 - Prob. 8PCh. 3.11 - Prob. 9PCh. 3.12 - Prob. 2PCh. 3.12 - Prob. 3PCh. 3.12 - Prob. 4PCh. 3 - Prob. 1RPCh. 3 - Prob. 2RPCh. 3 - Prob. 3RPCh. 3 - Prob. 4RPCh. 3 - Prob. 5RPCh. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - Prob. 8RPCh. 3 - Prob. 9RPCh. 3 - Prob. 10RPCh. 3 - Prob. 11RPCh. 3 - Prob. 12RPCh. 3 - Prob. 13RPCh. 3 - Prob. 14RPCh. 3 - Prob. 15RPCh. 3 - Prob. 16RPCh. 3 - Prob. 17RPCh. 3 - Prob. 18RPCh. 3 - Prob. 19RPCh. 3 - Prob. 20RPCh. 3 - Prob. 21RPCh. 3 - Prob. 22RPCh. 3 - Prob. 23RPCh. 3 - Prob. 24RPCh. 3 - Prob. 25RPCh. 3 - Prob. 26RPCh. 3 - Prob. 27RPCh. 3 - Prob. 28RPCh. 3 - Prob. 29RPCh. 3 - Prob. 30RPCh. 3 - Graphically find all solutions to the following...Ch. 3 - Prob. 32RPCh. 3 - Prob. 33RPCh. 3 - Prob. 34RPCh. 3 - Prob. 35RPCh. 3 - Prob. 36RPCh. 3 - Prob. 37RPCh. 3 - Prob. 38RPCh. 3 - Prob. 39RPCh. 3 - Prob. 40RPCh. 3 - Prob. 41RPCh. 3 - Prob. 42RPCh. 3 - Prob. 43RPCh. 3 - Prob. 44RPCh. 3 - Prob. 45RPCh. 3 - Prob. 46RPCh. 3 - Prob. 47RPCh. 3 - Prob. 48RPCh. 3 - Prob. 49RPCh. 3 - Prob. 50RPCh. 3 - Prob. 51RPCh. 3 - Prob. 52RPCh. 3 - Prob. 53RPCh. 3 - Prob. 54RPCh. 3 - Prob. 56RPCh. 3 - Prob. 57RPCh. 3 - Prob. 58RPCh. 3 - Prob. 59RPCh. 3 - Prob. 60RPCh. 3 - Prob. 61RPCh. 3 - Prob. 62RPCh. 3 - Prob. 63RP
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
- 2. A whisky distiller named Taketsuru Masataka puts 8000L of whisky into barrels for aging, with 200L of whisky per barrel. Each year the volume of whisky in each barrel reduces by 2% due to evaporation (this is known as the angels' share). For the first 11 years after barreling, Taketsuru sells 2 barrels for 20 dollars per litre at the end of each year. Write bn for for the volume of whisky in each barrel at the beginning of year n, write Un for the total volume of whisky in storage at the beginning of year n, and rn for the total revenue from selling whisky at the beginning of year n. (a) Find a direct formula for bn. (b) Calculate the values of v₁, v2, V3 and then find a recursive definition for Un. (c) Find a recursive definition for rn. (d) Write a MATLAB program to compute Un and rn for n = 1, 2 ... 12 and display the values in three columns n, rn, Un with appropriate headings. (e) At the end of the 12th year Taketsuru finds that he can sell 12-year old whisky at the higher price…arrow_forwardAt the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit. Table 2 Month Revenues ($) Bills ($) 1 400 600 2 800 500 3 300 500 4 300 250arrow_forwardAt the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit.arrow_forward
- A coal mine purchased 3 years ago for $7 million was estimated to contain 4,000,000 tons of coal. During the past 3 years the amount of coal removed was 21,000, 18,000, and 20,000 tons, respectively. The gross income obtained in these 3 years was $257,000 for the first year, $320,000 for the second year, and $340,000 for the third year. What is the cost depletion allowance for year 1.arrow_forwardPneumatics Engineering purchased a machine that had a fi rst cost of $40,000, an expected useful life of 8 years, a recovery period of 10 years, and a salvage value of $10,000. The operating cost of the machine is expected to be $15,000 per year. The inflation rate is 6% per year and the company’s MARR is 11% per year. Determine the depreciation charge for year 3 according to the straight line method. (UNITS ARE REQUIRED)arrow_forwardWilson Creek Farm has 200 acres of land available for planting. The owner is considering planting three crops: corn, soybeans, and wheat. The production yield, water requirements, and labor requirements for a salable crop are given here. The owner expects to have only 35,000 gallons of water available per week to use for the crops, and during the growing season he will only have 8000 person-hours of labor available. The expected profit per bushel of each crop is $1.00 for corn, $1.60 for soybeans, and $3.00 for wheat. The owner can use any mix of crops (i.e., he can plant the same crop on all 200 acres or he can plant all three crops in different proportions). d. Solve the problem using Excel Solver Tool. Add supporting pictures from the software for each step. Discuss your output in line with the given reports from Excel. Bushels/ Acre Water Required Produced (gal/acre/week) Crop 300 Corn Soybeans 200 Wheat 80 200 150 125 Person-Hours Labor Required/Acre 35 40 30arrow_forward
- During the tax season, every Friday, the J & J tax accounting firm provides assistance to people who prepare their own tax returns. Their charges are as follows:a. If a person has low income (<= 25,000) and the Consulting time is less than or equal to 30 minutes, there are no charges; otherwise the service charges are 40% of the regular hourly rate for the time over 30 minutes.b. For others, if the Consulting time is less than or equal to 20 minutes, there are no service charges; otherwise, service charges are 70% of the regular hourly rate for the time over 20 minutes.(For example, suppose that a person who has low income is spent 1 hour and 15 minutes, and the hourly rate is $70.00. Then the billing amount is $70.00 x 40 x (45/60) = $21.00). Write a program that prompts the user to enter the hourly rate, the total Consulting time, and whether the person has a low income. The program should output the building of Mount your program must contain a function that takes as input…arrow_forward. Employees of a certain firm are paid on hourly basis at the end of each week. If an employee works up to 40hrs, the employee is paid 6 GHS and 7 GHS per hour for a male and female respectively. If an employee works for more than 50 hours then the employee is also paid 2.5 the corresponding regular rate for hours worked in excess of 40. All employees are to pay 10 % of their gross as INCOME TAX and 2.5% towards the NHIS. If an employee has more than 3 children then he or she pays 2 cedis per child in excess of three towards GETFUND. Write a C++ program that can print onto screen the Net Salary of any staff onto screen. NB (NETSALARY is equal to gross salary less all deductions (VAT, NHIS, GETFUND). Write a C++ program and draw a flow chart for a software solution that can solve for the problem above.arrow_forwardAl 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: 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. 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. 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. 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 The credit facility is rejected for all other customers. Prepare a Decision Table for this hire- purchase schemearrow_forward
- Employees of KB and SONS Consultants Limited are paid at an hourly basics of 25GHS per an hour for regular hours and 1.5 times per hour for overtime hours in a week. Any hour worked over 40 hours per week is overtime. The following national tax sliding scale is then applied to determine the amount of tax to be paid by an employee. GrossWage Tax Rate (%) First 125 0 Next 125 5 Next 1500 10 Next 2750 15 Next 1250 20 Excess over 5000 30 In addition 6% of an employee’s gross wage is withheld for Social Security, 3% is withheld as constituency tax and 20GHS is withheld by the employer as welfare contribution. If an employee has more than 3 dependants then an amount of 5GHS for each dependant in excess of three towards NHIS. You are required to write a program that compute a workers gross pay, the deductions and his/her net pay. Your program should allow details of the staff to be accept /input into the system for the necessary computations. Try using comments in explaining the flow of the…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_forwardA person places $5000 in an account that accrues interest compounded continuously. Assuming no additional deposits or withdrawals, how much will be in the account after seven years if the interest rate is a constant 8.5 percent for the first four years and a constant 9.25 percent for the last three years?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