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Constraints and n variables. plier method of optimization of a problem involving- 14. The shape of a hol be of heighth anc tan a h/r, show t Formulation and Computational Exericses maximum if h= (F 15. A given quantity of semi-circular ends. S 1. Obtain the set of necessary conditions for the non-linear programming problem: Maximize Z-x+3x 5x subject to the constraints x+x, +3x, = 2; 5x, + 2x,2+ x35; the ratio of the len 2. If f-ax + b'x + cx where xx, + xx3+xx xx, show that the stationary value of f Tt/(JC+2). Use Lagr 16. Find the volume of ellipsoid x/a + occurs at x, = Eala, x, = Ealb, x= Lalc + x/E and (iii) Lagrange m 3. Use direct substitution method to minimize f(x,, x,) = (x, - 1)2 + (x, + 1) subject to i-x2-2 A cylinder is inscribed in a cone of height h. Apply direct substitution method to prove that the volume of the cylinder is maximum at height h/3. [Ans. Jmin-1/2 at x 1/2; x2-7/4] 17. Find the maximum xxx 1usin multipliers method 18. A meditation centre = Show that the rectangular solid of maximum volume that can be inscribed in a is cube. Use direct substitution method. sphere the square hall has b of regular pyramid i required for painting 6Show that, if the perimeter of a triangle is constant, the triangle has maximum area when it is equilateral. Use direct substitution method. 7. Show that the diameter of the right circular cylinder of greatest curved surface which can be substitution and (ii) inscribed in a given cone is equal to the radius of the cone. Use direct substitution method [Hint: Let r =radius of cone, a = semi-vertical angle of cone, h height of cylinder radius of cylinder, S curved surface of cylinder then maximize S 2Txh 19. A rectangular steel t the dimensions of th substitution (ii) Cons and x = subject h (r-x) cot a to 20. A window is to be d the perimeter is 40 ft. (i) Direct substitution Ans. Radius of se 80/(t+4) 8. Apply constrained variation method to prove that the volume of the biggest right circular sphere of given radius is 8/27 times that of the sphere. cone that can be inscribed in a 9. Use constrained variation to maximize the volume of an open cone when the surface cone is 20T area of the +h-20 0] 7 21. Find the volume of t of radius 'x'. Use (i [Hint: maximize V = 1/3Trh subject to nr multipliers method Use constrained variation to maximize the volume of a box made up of thin sheet metal 10. whose surface area is 24 maximize xyz subject to 2xy + 2yz + 2zx 24]

Constraints and n variables. plier method of optimization of a problem involving- 14. The shape of a hol be of heighth anc tan a h/r, show t Formulation and Computational Exericses maximum if h= (F 15. A given quantity of semi-circular ends. S 1. Obtain the set of necessary conditions for the non-linear programming problem: Maximize Z-x+3x 5x subject to the constraints x+x, +3x, = 2; 5x, + 2x,2+ x35; the ratio of the len 2. If f-ax + b'x + cx where xx, + xx3+xx xx, show that the stationary value of f Tt/(JC+2). Use Lagr 16. Find the volume of ellipsoid x/a + occurs at x, = Eala, x, = Ealb, x= Lalc + x/E and (iii) Lagrange m 3. Use direct substitution method to minimize f(x,, x,) = (x, - 1)2 + (x, + 1) subject to i-x2-2 A cylinder is inscribed in a cone of height h. Apply direct substitution method to prove that the volume of the cylinder is maximum at height h/3. [Ans. Jmin-1/2 at x 1/2; x2-7/4] 17. Find the maximum xxx 1usin multipliers method 18. A meditation centre = Show that the rectangular solid of maximum volume that can be inscribed in a is cube. Use direct substitution method. sphere the square hall has b of regular pyramid i required for painting 6Show that, if the perimeter of a triangle is constant, the triangle has maximum area when it is equilateral. Use direct substitution method. 7. Show that the diameter of the right circular cylinder of greatest curved surface which can be substitution and (ii) inscribed in a given cone is equal to the radius of the cone. Use direct substitution method [Hint: Let r =radius of cone, a = semi-vertical angle of cone, h height of cylinder radius of cylinder, S curved surface of cylinder then maximize S 2Txh 19. A rectangular steel t the dimensions of th substitution (ii) Cons and x = subject h (r-x) cot a to 20. A window is to be d the perimeter is 40 ft. (i) Direct substitution Ans. Radius of se 80/(t+4) 8. Apply constrained variation method to prove that the volume of the biggest right circular sphere of given radius is 8/27 times that of the sphere. cone that can be inscribed in a 9. Use constrained variation to maximize the volume of an open cone when the surface cone is 20T area of the +h-20 0] 7 21. Find the volume of t of radius 'x'. Use (i [Hint: maximize V = 1/3Trh subject to nr multipliers method Use constrained variation to maximize the volume of a box made up of thin sheet metal 10. whose surface area is 24 maximize xyz subject to 2xy + 2yz + 2zx 24]

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.FOM: Focus On Modeling: Linear Programming
Problem 16P: Feasible RegionAll parts of this problem refer to the following feasible region and objective...
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Constraints and n variables. plier method of optimization of a problem involving- 14. The shape of a hol be of heighth anc tan a h/r, show t Formulation and Computational Exericses maximum if h= (F 15. A given quantity of semi-circular ends. S 1. Obtain the set of necessary conditions for the non-linear programming problem: Maximize Z-x+3x 5x subject to the constraints x+x, +3x, = 2; 5x, + 2x,2+ x35; the ratio of the len 2. If f-ax + b'x + cx where xx, + xx3+xx xx, show that the stationary value of f Tt/(JC+2). Use Lagr 16. Find the volume of ellipsoid x/a + occurs at x, = Eala, x, = Ealb, x= Lalc + x/E and (iii) Lagrange m 3. Use direct substitution method to minimize f(x,, x,) = (x, - 1)2 + (x, + 1) subject to i-x2-2 A cylinder is inscribed in a cone of height h. Apply direct substitution method to prove that the volume of the cylinder is maximum at height h/3. [Ans. Jmin-1/2 at x 1/2; x2-7/4] 17. Find the maximum xxx 1usin multipliers method 18. A meditation centre = Show that the rectangular solid of maximum volume that can be inscribed in a is cube. Use direct substitution method. sphere the square hall has b of regular pyramid i required for painting 6Show that, if the perimeter of a triangle is constant, the triangle has maximum area when it is equilateral. Use direct substitution method. 7. Show that the diameter of the right circular cylinder of greatest curved surface which can be substitution and (ii) inscribed in a given cone is equal to the radius of the cone. Use direct substitution method [Hint: Let r =radius of cone, a = semi-vertical angle of cone, h height of cylinder radius of cylinder, S curved surface of cylinder then maximize S 2Txh 19. A rectangular steel t the dimensions of th substitution (ii) Cons and x = subject h (r-x) cot a to 20. A window is to be d the perimeter is 40 ft. (i) Direct substitution Ans. Radius of se 80/(t+4) 8. Apply constrained variation method to prove that the volume of the biggest right circular sphere of given radius is 8/27 times that of the sphere. cone that can be inscribed in a 9. Use constrained variation to maximize the volume of an open cone when the surface cone is 20T area of the +h-20 0] 7 21. Find the volume of t of radius 'x'. Use (i [Hint: maximize V = 1/3Trh subject to nr multipliers method Use constrained variation to maximize the volume of a box made up of thin sheet metal 10. whose surface area is 24 maximize xyz subject to 2xy + 2yz + 2zx 24]
Transcribed Image Text:Constraints and n variables. plier method of optimization of a problem involving- 14. The shape of a hol be of heighth anc tan a h/r, show t Formulation and Computational Exericses maximum if h= (F 15. A given quantity of semi-circular ends. S 1. Obtain the set of necessary conditions for the non-linear programming problem: Maximize Z-x+3x 5x subject to the constraints x+x, +3x, = 2; 5x, + 2x,2+ x35; the ratio of the len 2. If f-ax + b'x + cx where xx, + xx3+xx xx, show that the stationary value of f Tt/(JC+2). Use Lagr 16. Find the volume of ellipsoid x/a + occurs at x, = Eala, x, = Ealb, x= Lalc + x/E and (iii) Lagrange m 3. Use direct substitution method to minimize f(x,, x,) = (x, - 1)2 + (x, + 1) subject to i-x2-2 A cylinder is inscribed in a cone of height h. Apply direct substitution method to prove that the volume of the cylinder is maximum at height h/3. [Ans. Jmin-1/2 at x 1/2; x2-7/4] 17. Find the maximum xxx 1usin multipliers method 18. A meditation centre = Show that the rectangular solid of maximum volume that can be inscribed in a is cube. Use direct substitution method. sphere the square hall has b of regular pyramid i required for painting 6Show that, if the perimeter of a triangle is constant, the triangle has maximum area when it is equilateral. Use direct substitution method. 7. Show that the diameter of the right circular cylinder of greatest curved surface which can be substitution and (ii) inscribed in a given cone is equal to the radius of the cone. Use direct substitution method [Hint: Let r =radius of cone, a = semi-vertical angle of cone, h height of cylinder radius of cylinder, S curved surface of cylinder then maximize S 2Txh 19. A rectangular steel t the dimensions of th substitution (ii) Cons and x = subject h (r-x) cot a to 20. A window is to be d the perimeter is 40 ft. (i) Direct substitution Ans. Radius of se 80/(t+4) 8. Apply constrained variation method to prove that the volume of the biggest right circular sphere of given radius is 8/27 times that of the sphere. cone that can be inscribed in a 9. Use constrained variation to maximize the volume of an open cone when the surface cone is 20T area of the +h-20 0] 7 21. Find the volume of t of radius 'x'. Use (i [Hint: maximize V = 1/3Trh subject to nr multipliers method Use constrained variation to maximize the volume of a box made up of thin sheet metal 10. whose surface area is 24 maximize xyz subject to 2xy + 2yz + 2zx 24]
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