A company manufactures two products X and Y on three machinesTurning, Milling and finishing machines. Each unit of X takes, 10 hoursof turning machine capacity, 5 hours of milling machine capacity and 1hour of finishing machine capacity. One unit of Y takes 6 hours ofturning machine capacity, 10 hours of milling machine capacity and 2hours of finishing machine capacity. The company has 2500 hours ofturning machine capacity, 2000 hours of milling machine capacity and500 hours of finishing machine capacity in the coming planning period.The profit contribution of product X and Y are RS.23 per unit and Rs.32unit11perrespectively. Formulate the problem as the linear programmingproblem and find the maximum profit.(OR)

Answered: Image /qna-images/answer/879cdb6c-fb80-4700-9f99-edcd3a21f315.jpg

Answered: A company manufactures two products X…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A company manufactures three types of leather belts, namely A B and C. The unit profits from these three varieties are 10, 5 and 7 respectivel Leather is sufficient for only S00 belts per day (all types together) Belt A requires thrice the time of belt B and belt C requires twice the time of B. If all the belts of type B are produced, a maximum of 1,000 belts per day can be produced. Belt A requires a fancy buckle and 150 such buckles per day are availlable. There are sufficient number of buckles for the other varieties. Determine using simplex method, how many belts of each type be produced to maximize the total profit.
Infotron Inc makes electronic hockey and soccer games. Each hockey game requires 2 labor-hours of assembly and 2 labor-hours of testing. Each soccer game requires 3 labor-hours of assembly and 1 labor-hour of testing. Each day there are 63 labor-hours available for assembly and 33 labor-hours available for testing. How many of each game should Infotron produce each day to maximize its total daily output?
The 1-Dream company makes two different BLU-ray players, which are assembled on two different assembly lines. Line 1 can assemble 40 units of the BLU-Ray player and 55 units of the BLU-Ray player with DVR per hour, and line 2 can assemble 110 units of the BLU-Ray player and 195 units of the BLU-Ray player with DVR per hour. The company needs to produce at least 3,989 BLU-Ray players and 6,755 BLU-Ray player with DVR to fill an existing order. It cost $100 per hour to run line 1 and $310 per hour to run line 2, how many hours should each line run to fill the order at minimum cost? (Use x for line 1 hours and y for line 2 hours.) Minimize C= ≥ 3,989 6, 755 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round hours to 1 decimal place and cost to 2 decimal places. Number of hours to run line 1 is Minimum cost is $ Number of hours to run line 2…
company manufactures bamboo toy chairs and chess sets. Each bamboo toy chair yields a profit of $3, and each chess set, $5. A bamboo toy chair requires 5 hours of processing at Machine A and three hours at Machine B, and one hour at Machine C, while a chess set requires seven hours at Machine A, sixhours at Machine B, and two hours at Machine C.Machine A has a maximum of 130 hours of available capacity per day. Machine B has 90 hours, and Machine C has 25 hours.If the company wishes to maximize profit, how many bamboo toy chairs and chess sets should be produced per day?
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 12 units of carbohydrates, and no more than 11 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package. a. Write a system of inequalities to express the conditions of the problem. b. Graph the feasible region of the system. a. Fill in the chart. Protein Carbohydrates Fat Fruit unit(s) per ounce unit(s) per ounce unit(s) per ounce Nuts unit(s) per ounce unit(s) per ounce unit(s) per ounce .. Requirements per package At least At least No more than unit(s) unit(s) unit(s)
A factory that produces hygiene materials produces hygiene packages with three different contents, namely individual, family, xl-family, from masks, disinfectants and soap products. Stocks of hygiene products vary from week to week. For this reason, the factory applies a different production schedule for each week. For example, for the next week, how many boxes of individual, family and xl-family hygiene packages can they produce and put up for sale by using 270 thousand masks, 130 thousand disinfectants and 85 thousand soaps? Use the Gaussian Seidal method to reach the solution with an error of 0.1. Let the initial values for mask, disinfectant and soap are given as 49, 19 and 4, respectively. The amount of products in the packages is given in the table.(Note: do not use the values in thousands when trading.You can take 270, 230 and 85)
A shoe company manufactures two types of shoes: tennis and basketball. Each shoe requires the use of two operations, stitching and coloring, and there are at most 28 hours available each day for each operation. A pair of tennis shoes requires 2 hours of stitching and 2 hours of coloring, while a pair of basketball shoes needs 1 hour of stitching and 2 hours of coloring. Due to other restrictions, the company can make at most 183 pairs of shoes a day. Additionally, due to a sponsorship agreement, the company needs to produce at least 4 pairs of tennis shoes for each pair of basketball shoes. The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.)
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 6 units of protein 4 units of carbohydrates, and 4 unit of fat, and will contain 18 calories. Each K ounce of nuts will supply 3 units of protein, 3 unit of carbohydrate, and 5 units of fat, and will contain 29 calories. Every package must provide at least 6 units of protein, at least 10 units of carbohydrates, and no more than 11 units of fat. What is the least number of calories possible in a package? Write out the inequality for protein using x and y as your variables for ounces of fruit and nuts respectively (Use variables in order) Write out the inequality for carbohydrates using x and y as your variables for ounces of fruit and nuts respectively (Use variables in order) 0 Write out the inequality for fat using x and y as your variables for ounces of fruita my instructor srespectively (Use variables in order)
Infotron Inc makes electronic hockey and soccer games. Each hockey game requires 2 labor-hours of assembly and 2 labor-hours of testing. Each soccer game requires 3 labor-hours of assembly and 1 labor-hour of testing. Each day there are 48 labor-hours available for assembly and 36 labor-hours available for testing. How many of each game should Infotron produce each day to maximize its total daily output?
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, and 2 units of fat, and will contain 40 calories. Each ounce of nuts will supply 2 units of protein, 1 unit of carbohydrate, and 4 units of fat, and will contain 50 calories. Every package must provide at least 2 units of protein, at least 13 units of carbohydrates, and no more than 16 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories? Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized? Z=
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 using linear program solver.
XYZ Corporation operates two plants, each of which has a capacity of 200 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 17 units per day while customer D has a demand of 349 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 25 19 12 14 Plant 2 15 21 23 20 How many units should XYZ ship from each plant to each customer?

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