Number 6 linear Polygram C(S) = 8(0) + 6(100) = 600is that the maximum value of C is 640. This is false! There is, since isocost lines with arbitrarily large values of C intersect theasimi2x – y < 20s*,y 2 06. MinimizeZ = 20x + 30ysiminiM SIsubject to2x +y < 103x +4y < 248x + 7y > 56x, y 2 07. MinimizeC=5x+yy0l noltoubor1subject togol geinnige2x - y 2 -24x + 3y < 12x- y = -1x, y 2 08. Maximize

Answered: Image /qna-images/answer/5159a485-dfc2-438f-92a0-312f2aeedc52.jpg

Answered: 6. Minimize Z = 20x + 30y %3D asiminiM…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 17EQ

See similar textbooks

Similar questions

Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.
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).
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.
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.
Minimize f(x,y,z)=xyz subject to constraints x^2+y^2=0 and x_z=0, by using the method of Lagrange Multipliers ?
Find the minimum value of f(x,y)=x^2+y^2 subject to the constraint 6x+4y=18 using the method of Lagrange multipliers and evaluate λ. minimum f = ? λ = ?
Use Lagrange multipliers to find the maximum and minimum values of f (x, y, z) = x2 + 2y2 + 3z2 subject tox + y + z = 1 and x - y + 2z = 2.
Suppose that a temperature of a metal plate is given by T(x,y)=x2+2x+y2, for points (x,y) on the elliptic plate defined by 6x2+5y2≤60. Find the maximum and minimum temperatures on the plate. Use Lagrange Multipliers to determine the absolute extrema of f on the indicated constraint.
Although ∇ƒ = l∇g is a necessary condition for the occurrence of an ex-treme value of ƒ(x, y) subject to the conditions g(x, y) = 0 and ∇g ≠ 0, it does not in itself guarantee that one exists. As a case in point, try using the method of Lagrange multipliers to find a maximum value of ƒ(x, y) = x + y subject to the constraint that xy = 16. The method will identify the two points (4, 4) and (-4, -4) as candidates for the location of extreme values. Yet the sum x + y has no maximum value on the hyperbola xy = 16. The farther you go from the origin on this hyperbola in the first quadrant, the larger the sum ƒ(x, y) = x + y becomes.
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.
Find the point on the surface 4x+y-1=0 closest to the point (1,2,-3) using Larange Multipliers. I have only managed to determine that z=-3, but all the other x and y values I have solved for have not looked right compared to a graph.
Find the minimum value of z =x2 + y2 subject to the condition x + y = 18.

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

6. Minimize Z = 20x + 30y %3D asiminiM subject to 2x +y < 10 3x + 4y < 24 8x + 7y > 56 x, y 2 0 7. Minimize