Concept explainers
Explanation of Solution
Consider the LP problem of HAL computer considering the projects that should be started. Data related to each of the project tabulated.
Consider the following variables
HAL has the following goals
Goal 1:
The total NPV of all chosen should be at least
Goal 2:
The average probability of success for all projects chosen should be at least 0.75. Thus the constraint becomes,
Goal 3:
The average growth rate of all projects chosen should be at least 15%. Thus the constraint becomes,
Goal 4:
The total cost of all chosen project should be at most $1billion. Thus the constraint becomes,
Hence the LP is formulated as given below
Minimize,
Subjected to the constraints,
From the above equations it is found that these set of constraints there is no feasible region. That is all constraints cannot be met. So assign a cost value incurred if any of the priorities or goal is not met. So, introduce the following deviational variables.
Hence the constraints become,
Giving lowest priority to goal 4 and highest priority to goal 1, assign weight to each goal
Now, the goal is to minimize the deviation from each goal
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Introduction to mathematical programming
- Assuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he/she completes university. If he/she does not complete university, the payment is stopped at the time he/she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, and invest GHC 70 a month till age 30 years. If the person does not complete the apprenticeship, the payment is stopped at the time he/she exited. Remember that persons who are less than 18 years or 30 years and above do NOT qualify to enroll on this program. You are to write a c++ program for the above scenario. Your program should a) compute the total investment made for the person if he/she either finishes or exited along the way. b) display the results.arrow_forwardDetermine the probable cost per hour of owning and operating a scraper unit with a 200-hp diesel engine. Use the combined depreciation and investment cost method to calculate ownership costs. 1. Calculate owning and operating costs with operator per hour of use. 2. Calculate cost per cy of material per hour. The following conditions apply: Factory delivered price = $300,000 Sales tax = 6% of delivered price Operating factor = 0.60 Fuel costs = $5.23/gal Unloading and assembling = $2,500 Salvage value = $20,000 Useful life= 4 yr Hours used per year = 2,000 hrs Investment costs = 3% of average annual value Maintenance and repairs = 50% of straight- line depreciation Diesel engine = 200hp Crankcase oil capacity = 9 gal Hours between oil changes = 120 hrs Oil costs = $14/gal Tires= $62,000 Tire life = 4000 hrs Tire repairs = 15% of tire depreciation Operator cost= $35/hr Equipment capacity = 85 cy/hrarrow_forwardThe Touche Young accounting firm must complete three jobs during the next month. Job 1 will require 500 hours of work, job 2 will require 300 hours of work, and job 3 will require 100 hours of work. Currently, the firm consists of 5 partners, 5 senior employees, and 5 junior employees, each of whom can work up to 40 hours per month. The dollar amount (per hour) that the company can bill depends on the type of accountant who is assigned to each job, as shown in the table below. (The X indicates that a junior employee does not have enough experience to work on job 1.) All jobs must be completed. Touche Young has also set the following goals, listed in order of priority: Goal 1: Monthly billings should exceed $68,000. Goal 2: At most, 1 partner should be hired. Goal 3: At most, 3 senior employees should be hired. Goal 4: At most, 5 junior employees should be hired. Formulate a preemptive goal programming model for thissituationarrow_forward
- 4 A computer company produces hardware and software using the same plant and labor. The total cost of producing computer processing units H and software programs S is given by TC=aH+bS−cHS For the product-specific case for software, the firm experiencesarrow_forwardG-Motor manufactures airplane engines and has an annual capacity of ? units. For the current production facilities, the company has an annual cost of $?? million. G-motor plans to expand its current aircraft engine capacity in light of anticipated growth in aircraft engine demand in the coming years. The company intends to expand its manufacturing capacity by establishing new facilities. Production facilities can be set up in two ways (called as type A and type B). While the cost of establishing a type A manufacturing facility in any given year is $??, the production capacity of such a facility is ?? units. The cost of establishing a Type B manufacturing facility is $??, and the anticipated production capacity is ?? units. Annual expenditures for any facility of type A or B are projected to be $? million dollars. G-Motor aims to make a decision about the establishment of a new facility during the planned period t=2022, 2023,...,T. The demand for aircraft engines in the coming years is…arrow_forwardA software company has 3 senior developers and 4 junior developers. These developers are working as 3 different teams; 2 sets of ‘1Senior+1Junior’ and 1 set of ‘1Senior+2Junior’. Productivity levels of junior developers according to their senior developer working with are given in the table. Formulate this problem as an LP model. Senior D. 1 Senior D. 2 Senior D. 3 Junior D. 1 2 10 5 Junior D. 2 6 9 8 Junior D. 3 7 5 6 Junior D. 4 10 6 10arrow_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_forwardAssuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he / she completes university. If he / she does not complete university. If he / she does not complete university, the payment is stopped at the time theta / she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, the person who are less than 18 years or 30 years and above do not qualify to enroll in the program. a. Request a persons name, age, what he / she wants to do (go to school or learn a trade), time of exit if any and disqualify the person if he / she does not meet the age criteria b. Compute the total investment made for the person if he / she either finishes or exited along the way c. Display the results d. Explain the…arrow_forwardQuestion 4An electronics shop sells 6000 headphones in a year and the sales is relatively constantthroughout the year. These headphones are purchased for SR 20.00 each, and the leadtime is three days. The holding cost per headphone per year is 10% of the unit cost andthe ordering cost per order is SR 75. There are 300 working days per year. Calculate thefollowing:(i) What is the annual holding cost?(ii) In minimizing the cost, how many orders would be made each year?(iii) Given the EOQ, what is the total annual inventory cost (including purchase cost)?(iv) What is the time between orders?(v) What is the ROP?arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole