A system composed of two industries, coal and steel, has the following input requirements.(a) To produce $1.00 worth of output, the coal industry requires $0.20 of its own product and $0.40 of steel.(b) To produce $1.00 worth of output, the steel industry requires $0.30 of its own product and $0.40 of coal.STEP 1: Find D, the input-output matrix for this system.CoalSteelD =0.20.4X =0.40.3STEP 2: Solve for the output matrix X in the equation X = DX + E, where E is the external demand matrix E =ECoalCoalSteelSteel10,00020,000

Given the input requirements.(a) To produce $1.00 worth of output, the coal industry requires $0.20…

Answered: A system composed of two industries,…

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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Consider the following two systems. (b) A-¹ - 4x + 2y 2x + y = - 4x + 2y 2x + y 3 = -1 -1 = (i) Find the inverse of the (common) coefficient matrix of the two systems.
1. Please do not reject my questions, its simple to understand and help me. Please show your calculations step by step on how you get to the answers please. A. For this question, use k = 29, p = 3 and s = 8. Replace the values k, p and s in the following system of linear equations: Answer the following questions. B)Give the matrix of coefficients A of this system and its augmented matrix [A|b) (use your numerical values k, p and s in your matrices). C) Use the Gauss-Jordan algorithm to calculate the staggered-reduced form of the augmented matrix (Alb).
Given the traffic flow diagram below (with numbers representing vehicles per hour): 100 100 X₁ 4 X5 X₂ 50 100 X3 X4 50 (a) Write out a linear system equivalent to this flow pattern. (b) Write out the matrix of coefficients and the augmented matrix that corresponds to your system in part (a). Note: you do not have to solve this system.
Frankie has a very busy lunch counter. On Tuesday, they sold 279 meals and brought in revenue of $2,347. The vegetarian curry rice costs $7.00 and the Chicken Marsala costs $12.00. If the augmented matrix is given by 1 a b 7 c d What is the value of d
The strength requirements for various materials (steel, concrete,wood) in a multi-component system are interconnected. The strengths of the materials are given by the following equations:3x−y+2z=15002x+2y−z=12004x-2y+z=1600Additionally, there is a cost factor associated with each material. The costs per ton are: Steel: $4000 Concrete: $1500 Wood: $1000 Use a matrix method to find the optimal combination of materials that meets the strength requirements while minimizing the cost. The total cost of the materials is represented by the dot product of the material amounts vector [x, y, z]and thecost vector.
12.
You have three types of ground coffee: cheap ($5/pound), medium ($8/pound), and expensive Arabica ($14/pound). You want to make a blend that costs $10/pound, and you want to make 50 pounds of it. You also want to be able to say "contains 20% Arabica" without lying. Set up and solve a linear system to find out how much of each type of coffee you should use, while spending the least money.

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