Rewrite the following optimization problem in standard form:maximize 5x + 7ys.t.2x + 4y ≤ 116x - 2y = 8x, y ≥ 0Next, write the problem using matrix notation and specify the c, b, A matrices.

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Answered: Rewrite the following optimization…

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 small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the…

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Rewrite the following optimization problem in standard form: maximize 5x + 7y s.t. 2x + 4y ≤ 11 6x - 2y = 8 x, y ≥0 Next, write the problem using matrix notation and specify the c, b, A matrices.