A factory produces two types of widgets: Type A and Type B. The factory uses theGauss-Seidel method to optimize the production process. Type A widgets require3 units of material and 2 hours of labor to produce, while Type B widgets require4 units of material and 1 hour of labor. The factory has a daily limit of 120 units ofmaterial and 8 hours of labor. In addition, the factory has a daily demand for atleast 100 Type A widgets and 50 Type B widgets. Using the Gauss-Seidel method,determine the maximum number of Type A and Type B widgets he factory canproduce in a day while still meeting the daily demand and staying within the dailylimits of material and labor.

Given that, A factory produces two types of widgets: Type A and Type B. The factory uses the…

Answered: A factory produces two types of…

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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An energy company uses three different processes for generating electricity. One of the processes uses wind energy (and so requires no fuel), while the other two consume a combination of biofuel and natural gas. Each process also requires some amount of labour and emits some amount of carbon dioxide. The amount of biofuel (in Mg) and natural gas (in mcf = mega cubic feet) consumed, the labour required (in person-hours), the carbon dioxide (CO₂) emitted (in Mg), and the power generated (in MWh) per day of operation of each process is as follows: Process 1 2 3 Electricity generated 20 32 85 CO₂ produced 0 12 29 Labour Biofuel required required 20 0 13 10 18 30 Natural gas required 0 15 40 Each MWh of electricity can be sold at £144 and there is no limit on the amount that can be sold. Over its next planning period, the company has 320 person-hours for labour, 75 Mg of biofuel, and 90 mcf of natural gas available. (a) The company emits all the CO₂ it produces into the atmosphere. Due to…
I need C pls
A manufacturer produces three products: Product A, Product B and Product C. Tobe able to produce each product he uses a combination of three distinct inputsnamely Input I, Input II and Input III the supply of which is currently at 730, 350and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3units of Input II and 4 units of Input III to be produced. Similarly, each unit ofProduct B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5units of Input I, 1 unit of Input II and 3 units of Input III.(i) Let a, b and c represent the number of units produced of Products A, B and Crespectively. The manufacturer must decide what quantity of each product toproduce so that his entire supply of inputs is utilized. Formulate his/herdecision in the form of a system of three linear equations in the variables a, band c. [3 marks](ii) Rewrite the above system of linear equations in the matrix form Ax = b. [2 marks](iii) Hence or otherwise, determine how…
A drug company manufactures two kinds of sleeping pill: Pill 1 and Pill 2. The pills contain a mixture of two different chemicals, A and B (and no other ingredients). Pill 1 must contain at least 65% Chemical A and Pill 2 must contain at least 55% Chemical A. There are two different ways to produce Chemicals A and B. Operating Process P requires 7 Kgs of A raw material to run for one hour and 2 hours of labor time (because it must be supervised by 2 workers). Operating Process Q requires 5 Kgs of A raw material to run for one hour and 3 hours of labor time. Operating Process P produces three Kgs of each chemical for one hour runtime. Operating Process Q produces 3 Kgs of Chemical A and one Kg of Chemical B for one hour runtime. There are L > 0 hours of labor and R > 0 Kgs of raw material available. The company earns A profit from Pill i of πi ≥ 0 (i = 1,2) Kshs per Kg. The company wishes to find a production plan that maximizes the profit it makes from manufacturing sleeping…
Prime Paints manufactures two types of paints, one for interior painting and the other for exterior painting. Both types require the use of two raw materials - M1 and M2, so that the maximum daily availabilities of these materials are 24 tons and 6 tons, respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tons of M1 and 1 ton of M2. It has been established that the daily demand for interior paint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. The company wants to determine the optimum product mix of interior and exterior paints to maximize the total daily profit given that the profit per ton of the interior paint is 4 thousand dollars and the profit per ton of the exterior paint is 5 thousand dollars.
Find the production schedule for the technology matrix and demand vector given below:
Find the production schedule for the technology matrix and demand vector given below: 0.1 0.3 0.4 4 A = 0.1 0.2 0.4 D = 5 %3D 0.1 0.1 3 X =
C and D
A logistics company wants to transport wood from 3 forestry centers to 5 demand centers. Transportation costs (in euros) are shown in the following table along with production and demand at each center: F1 F2 F3 Demand D1 100 350 300 10 D2 200 300 200 20 D3 400 600 450 16 D4 350 700 300 20 D5 Production 150 500 200 7 30 20 28 What is the transportation program that minimizes the total transportation cost? Obtain an initial solution with the least cost method. Find the transportation schedule that minimizes the total transportation cost. Report the minimum total transportation cost. Indicate whether there are alternative optimal solutions, and if so, it obtains them. Please be as clear as possible. Explain all the steps of the problem. Answer all the points requested. Thank you very much.|

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