1. A milk plant manufactures two types of products A and B and sells them at a profit of Rs. 5 on type A and Rs. 3 on type B. Each product is processed on two machines G and H. Type A requires one minute of processing time on G and two minutes on H; type B requires one minute on G and one minute on H. The machine G is available for not more than 6 hours 40 minutes, while machine B is available for 8 hours 20 minutes during any working day; formulate the problem as LP problem.

1. A milk plant manufactures two types of products A and B and sells them at a profit of Rs. 5 on type A and Rs. 3 on type B. Each product is processed on two machines G and H. Type A requires one minute of processing time on G and two minutes on H; type B requires one minute on G and one minute on H. The machine G is available for not more than 6 hours 40 minutes, while machine B is available for 8 hours 20 minutes during any working day; formulate the problem as LP problem.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 73P

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Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.
A gold processor has two (2) sources of gold ore, Source A and source B. To keep his plantrunning, at least three (3) tons of ore must be processed each day. Ore from A costs $20 per tonto process, and ore from B costs $10 per ton to process. Costs must be kept to less than $80 perday. Moreover, Federal Regulations require that number of ore from source B cannot exceedtwice the number of ore from source A. If ore from source A yields 2 oz. of gold per ton, andfrom source B yields 3 oz. of gold per ton, how many tons of ore from both sources must beprocessed each day to maximize the amount of gold to the above constraints?
4) A printing company makes three grades of wall posters. The better-quality posters sell for Rs. 2.50, intermediate quality for Rs.2.00 and the poorer quality poster for Rs. 1.50. Paper costs Rs. 0.75 for each of the better-quality posters and Rs.0.50 and Rs. 0.25 for each intermediate and poorer quality poster respectively. Because of poor quality paper, the less expensive posters require two minutes of printing time while the other two require 1 minute of printing time only. The department is allocated Rs.150 per day for paper. There are 480 minutes of printing time available daily and each minute that is used to estimate to cost the company Rs. 0.25. In addition, the department incurs a fixed daily cost of Rs. 125, which are not affected by the quantity and quality of papers produced. You are asked to suggest as to how much each type of posters is to produce in order to maximize daily profit?(Don't use excel shortcut solve manually by Simplex LPP method)
1) A company produces drinks in liters (33.8 oz.) and single serving (16.9 oz.) containers that utilize three resources of soda, plastic for the containers, and manufacturing time. The liter requires 3 ounces of plastic and the single-serving container requires 1.5 ounces of plastic, while the liter requires a total of 2 minutes of manufacturing time and a single serving requires 90 seconds of manufacturing time. Each week, the company has 55,000 ounces of soda available, 6,000 ounces of plastic, and 40 hours of manufacturing time. Each liter has a profit of $0.70 and each single serving has a profit of $0.50. a. Write the Linear Program. Please write out the work in excel
4 Sunco processes oil into aviation fuel and heating oil. Itcosts $40 to purchase each 1,000 barrels of oil, which isthen distilled and yields 500 barrels of aviation fuel and 500barrels of heating oil. Output from the distillation may besold directly or processed in the catalytic cracker. If soldafter distillation without further processing, aviation fuelsells for $60 per 1,000 barrels, and heating oil sells for $40per 1,000 barrels. It takes 1 hour to process 1,000 barrels ofaviation fuel in the catalytic cracker, and these 1,000 barrelscan be sold for $130. It takes 45 minutes to process 1,000barrels of heating oil in the cracker, and these 1,000 barrelscan be sold for $90. Each day, at most 20,000 barrels of oilcan be purchased, and 8 hours of cracker time are available.Formulate an LP to maximize Sunco’s profits.
1. A distillery produces two types of alcohol for filling and distributing, the regular beer and the premium beer. A batch of regular costs $375 to manufacture and a container of the Premium beer costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material. Each batch of regular beer requires 4 hours processing whereas each batch of premium requires 2 hours of processing. Further each batch of regular requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of regular and a batch of Super each require 1 litre of material. Processing and testing have a maximum of 100 and 180 hours available and the total material available is 40 litres. Because of an agreement, the sales of regular beer are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of premium beer must be sold each week.…
1.A clockmaker makes two types of woodenclocksto sell at various malls. It takes him three hours to assemble a pine clock, which requires two oz of varnish. It takes four hours to assemblea molave clock, which takes four oz of varnish. He has eight oz of varnish available in stock and can work 12 hours. If he makes a P100 profit on each pine clock and P120 on each molave clock, how many of each type should he make to maximize his profit?2.A biologist is developing two new strains of bacteria. Each sample of Type A bacteria produces five new viable bacteria,and each Type B bacteria produces six new viable bacteria. Altogether, at least 150 new viable bacteria must be produced. At least 10, but not more than 20,of the original sample,must be Type A,and not more than 60 of the samples must be Type B. A sample of Type A costs P500,and a sample of Type B costs P700. If both types are to be used, how many samples of each type should be used to minimize the cost?
4. Barrows Textile Mills produces two types of cotton cloth— denim and corduroy.Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of rawcotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard ofcorduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours.Although the demand for denim is practically unlimited, the maximum demand forcorduroy is 510 yards per month. The manufacturer has 6500 pounds of cotton and 3000hours of processing time available each month. The manufacturer makes a profit of$2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants toknow how many yards of each type of cloth to produce to maximize profit.
Although the problems say solve graphically, please solve all problems using the QM for Windows software or solve manually. B.6 The Christina Alvarez Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc, the company has available a total of 25.000 Ib of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 Ib of steel and 20 lb of zinc, and each yields a profit of 590. Each model B gate requires 100 1b of steel and 30 ib of zinc and can be sold for a profit of $70. Find by graphical IP the best production mix of yard gates.
An XYZ company has a W, H, O plant with a monthly production capacity of 60 tons, 50 tons, and 42 tons, respectively; and has 3 sales warehouses in cities A, B, C, D Where each warehouse has a monthly requirement of 30 tons, 34 tons, 44 tons and 25 tons. With shipping cost W to ABCD = IDR 12,000,-, IDR. 8.000,-, Rp. 12.000,-, Rp. 14,000,-; H to A B C D = Rp. 8.000,-, Rp. 18.000,-, Rp. 10,000,-, Rp. 6.000,-; and O to ABCD = Rp. 16.000,-, Rp. 16.000,-, Rp. 2,000, Rp. 10,000,-. Please calculate using Vogel's Approximation Method or VAM Question a. What is the best transportation model in your opinion to solve the above problems? b. What is the minimum transportation cost to solve the shipping transportation problem! c. Based on these calculations, give suggestions regarding the transportation model and the amount of costs incurred by the company!
Show the complete Linear Programming Model. Show solutions (i.e. decision variables, objective function, subject to constraints, etc.) Q. A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $1,000 per ton to process, and ore from source B costs $500 per ton to process. Costs must be kept to less than $4,000 per day. Moreover, Government Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? Formulate the LP model.