Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Chapter 3.5, Problem 6P
Explanation of Solution
Formulation of LP:
Given,
Policeman can be hired to work either 12 consecutive hours/ 18 consecutive hours.
For day 1, part-1: 12 policeman for 6 hours.
For day 1, part-2: 8 police work for 6 hours.
Four members were useless (First hired)
First, these policeman were payed. That is as follows
Total 20, that is,
For day 1, part-3: 6 of the police work for 6 hours.
That is,
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Wilson 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
30
3. 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.
A 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).
Chapter 3 Solutions
Introduction to mathematical programming
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 Fincos 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 - Prob. 31RPCh. 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
Similar questions
- Pneumatics 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_forwardACE 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.arrow_forwardProblem 5. An Electricity board charges the following rates mentioned in the table for the use of electricity. All users are charged Taka 50 as a meter charge for every month. If any user wants to change/replace his meter, he will be charged taka 2000. The monthly bill will be generated based on ● Customer Category ● Consumed Units ● Phase ● For Category 3 and 5 along with other parameters, you need to also consider flat rate, peak time, and off-peak time. Take input from the user, how many units were consumed during flat rate, peak, or off-peak time. ● Meter Charge Write a program to read the name of the user, Customer Category, Phase, number of units consumed and print out the monthly bill. Note that ● Phase, flat rate, peak time and off-peak time will be appeared based on the customer category. ● The monthly bill will be calculated following the number of Days in a montharrow_forward
- Steelco manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differs for each mill. The time and cost for each mill are shown in the table below. Each month, Steelco must manufacture at least 500 tons of steel 1 and 600 tons of steel 2. Formulate an LP to minimize the cost of manufacturing the desired steel.arrow_forwardMississippi Agricultural Co. owns a wheat warehouse with a capacity of 20,000 bushels. At the beginning of month 1, they have 6,000 bushels of wheat. Each month, wheat can be bought and sold at the price per 1000 bushels given in the table below. The sequence of events during each month is as follows: i) The initial stock of wheat is counted. ii) Any amount of wheat up to your initial stock can be sold at the current month's selling price. iii) The company can buy (at the current month's buying price) as much wheat as they want, subject to the warehouse size limitation. Do the following: 1- Formulate an LP that can be used to determine how to maximize the profit earned over the next 10 months and. 2- Solve your LP using AMPL solver python. Month 1 2 3 4 5 6 7 8 9 10 Selling Price Purchase Price 3 6 7 1 4 5 5 1 3 2 ∞∞№343 8 8 2 325 10 2 5arrow_forwardamyo Manufacturing produces four parts that require the use of a lathe and a drillpress. The two machines operate 10 hours a day. The following table provides the time inminutes required by each part:It is desired to balance the two machines by limiting thedifference between their total operation times to at most 30 minutes. The market demand for each part is at least 10 units. Additionally, the number of units of part 1 may not exceed that of part 2. b)Solve the following problems by B&B:Maximize ?=18?1+14?2+8?3+4?4subject to15?1+12?2+7?3+4?4+?5≤37?1,?2,?3,?4,?5=(0,1) Part 6arrow_forward
- Comet Enterprises assembles hand-held vacuum cleaners and desk fans in Memphis, TN. Each vacuum cleaner requires one electric motor, 4 hours of labor, and 20 ounces of stainless steel, and brings $12 profit. Each fan requires one electric motor, 1 hour of labor, and 10 ounces of stainless steel, and brings $4 profit. There are 100 electric motors, 160 hours of labor, and 1100 ounces of stainless steel available for this week's production. (a) Formulate a linear program to determine Comet's production plan for this week to maximize total profit, that is, how many hand-held vacuum cleaners, and how many desk fans should the company produce.arrow_forwardThe 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 EXCELarrow_forwardDe anza is looking to hire teachers and TAs to fill its staffing needs for its summer program at minimum cost. The average monthly salary of a teacher is $2400 and the average monthly salary of a TA is $1100. The program can accommodate up to 45 staff members, needs at least 30 to run properly, and must have teachers (they will NOT employee only TAs). They must have at least 10 TAs and may have up to 3 TA’s for every 2 teachers. How many teachers and TAs the should the program hire to minimize costs. What is the minimum cost? use python code & explain each steparrow_forward
- De anza is looking to hire teachers and TAs to fill its staffing needs for its summer program at minimum cost. The average monthly salary of a teacher is $2400 and the average monthly salary of a TA is $1100. The program can accommodate up to 45 staff members, needs at least 30 to run properly, and must have teachers (they will NOT employee only TAs). They must have at least 10 TAs and may have up to 3 TA’s for every 2 teachers. How many teachers and TAs the should the program hire to minimize costs. What is the minimum cost? use code & explain each steparrow_forwardThe 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_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_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