Use technology to minimize the following:Minimize g = 1lyı + 9y2 + 10y3 subject toЗу1 + 5у2 + 29Уз — 64у2 + 2уз > 32y1 2 7Ул 2 0, у2 20, уз — 0If no solutions exist enter DNE in all answerboxes.Y1 =Y2 =Y39 =

Answered: Image /qna-images/answer/e9c64089-67a1-48ad-8a04-90331ce5e96e.jpg

Answered: Use technology to minimize the…

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 function, z = ax + by, is to be optimized subject to the constraint, x2 + y2=1 where a and b are positive constants. Use Lagrange multipliers to show that this problem has only one solution in the positive quadrant (i.e. in the region x > 0, y > 0) and that the optimal value of z is √a2 +b2.
Find the values of x and y that minimize 24x2+12xy+4y2+6x−4y+16 subject to the constraint 8x+2y+1=0. x=________, y=____________
A rectangular vault is to be constructed on an existing floor at a bank so as to enclose avolume of 485 cubic meters. The cost per square meter of materials is $2,000 for the ceiling,$9,000 for the wall with the door and $3,000 for the other three walls. The minimized costof the vault rounded to the nearest $1,000 dollars is:a. $964,000b. $971,000c. $982,000d. $993,000
Suppose measurements of y versus x give three points in the x-y plane withcoordinates (0,6), (1,0), (2,0). (a) Show that there is no straight line that intersects all three points. (b) Find the linear function y = c0 + c1x that best fits this data in the least squares sense, by finding the coefficients c0, c1 using the method of least squares. (c) Show that the solution is the best possible in the sense that it minimizes the length of the residual.
Find the minimum value of f (x, y) = xy subject to the constraint 5x - y = 4 in two ways: using Lagrange multipliers and setting y = 5x -4 in f(x,y).
Prove that if you minimize the square of the distancefrom the origin to a point (x, y) subject to the constraintg(x, y) = 0, you have minimized the distance from theorigin to (x, y) subject to the same constraint.
Solve max f( x,y , z) 3x2+y problem by means of Lagrange multipliers under the constraints of 4x-3y=9 and x2+z2=9. Explain what the values of Lagrange multipliers mean?
Suppose that we want to optimize the function V = x2 + y2 + z3, subject to the restriction xyz = 4, using the Lagrange multipliers technique. If λ corresponds to the multiplier used when defining the Lagrange function, then one of the equations of the system to be solved corresponds to:
Solve min x1-x2-2x3 problem by means of Lagrange multipliers under the constraints of x1+x2+x3=5 and x12+ x22 =4. Explain what the values of Lagrange multipliers mean?
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7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.
Give the optimal solution. Minimize z = 4x + 8y subject to: x + 1.5y ≥ 45 2x+ 0.5y≥ 40 x+y ≤ 40 x,y≥ 0

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Use technology to minimize the following: Minimize g 11yı + 9y2 + 10y3 subject to 3yı + 5y2 + 2y3 > 6 4y2 + 2y3 > 3 2y1 2 7 Ул 2 0, У2 20, Уз 2 0 If no solutions exist enter DNE in all answerboxes. Y1 = Y2 Уз g = || ||