Solve using Lagrange Multipliers, final answers should have 4 decimal places.Find the maximum and minimum values of f (x,y)= 3x -6y subject to the constraint 4x? + 2y? = 25%3D555/2with possible solutions on -s22

Answered: Image /qna-images/answer/41cdc636-aa2a-410c-8985-5862edb9524a.jpg

Answered: Solve using Lagrange Multipliers, final…

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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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.
Q3 A- Find all solutions to this equation (Plot to get rough estimates) N^6 N^3=2 B- Find all solutions for the following system of equations (Hint: Plot) SQRT(x) - SQRT(y) = 17 x- y = 85 C- Find a solution to the following set of equations (using any method you like) -3.0X1 -1.1X2 -2.0X3 -1.8X4 = 1.0 3.2x1 + 2.1X2 +3.2X3 +5.2X4 = 2.0 3.4X1 +2.4X2 -4.2X3 +3.2X4 = 8.0 2.6X1 +2.1X2 -3X3 +3.4X4 = -5.0 How sensitive is the solution to the value in the right hand side of first equation (if it changes from 1 to 1.1, or to 0.9 how does the solution changes)

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Solve using Lagrange Multipliers, final answers should have 4 decimal places. Find the maximum and minimum values of f (x,y)= 3x -6y subject to the constraint 4x? + 2y? = 25 5 5 5/2 with possible solutions on -s 2 2