Problem 1. Find the values of r, y that minimize x² + xy +y² - 2x - 5y

Q: Find the values of x Z which minimize 2 N/ 3xy ty and y subject to the constraint 3x-4-1=0

A: Finding Minimum Value Using Lagrange Multipliers Minimize the function f(x, y) = x²/2 - 3xy + y² +…

Q: 2. Maximize. z subject to 2x1 + 3x2 – 4x3 = 3x1 - 2x2 + x3 0, x2 > 0, x3 > 0.

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Q: minimize z=4x+6y subject to: 3 0 y > 0

A: We are going to solve the give. Problem by graphical method.  In the shaded region, the linear…

Q: Minimize C = 5x + 6y     subject to   4x  +  y  ≥ 36   2x  +  y  ≥ 30   x  +  3y  ≥ 30   x ≥ 0, y ≥…

A: NOTE: Refresh your page if you can't see any equations. . The given system is  subject to

Q: If a(x) = 4x² – 3 and b(x) =- Vx+3 what is a(b(x))? a(b(x)) = 2x a(b(x)) = = x-9 © a(b(x)) = *=²…

A: We are given: a(x)=4x2-3 and b(x)=x+34To find:a(b(x))

Q: Minimize C =-4x - 7y %3D Subject to 6x+ 2y < 40 2.x +3y < 50 x 20, y 2 0

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Q: Q1. By using simplex (Tabular) method, maximise f = 10x1 + 9x2 subjected to: 3x1 + 3x2 0

A: Consider the provided question, f=10x1+9x2subject to:3x1+3x2≤214x1+3x2+x4≤24x1,x2,x3,x4≥0

Q: 4. Minimize: Z = 3X₁ +5X₂ + 5X3 + 4X4 Subject to: 8X₁ + 2X4 ≤ 100 4X +3X - 90

A: Introduction: The simplex method is a method for testing vertices as potential solutions in a…

Q: Minimize C= 3x + 7y subject to x +3y >= 15                   4x + y >= 16                  X>=0,…

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Q: Minimize: =4x+5y Subject to: 10x 5y100 20x+10y 150 x+y12 0 y 20

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Q: If x² + 2y +3z1 = x2 + 2y2 + 3z2 = x3 + 2y3 +3z3 =2, and x₂x3 +2y2y3 +3z2z3 = x3x1 +2y3v1 +3Z3Z1 =…

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Q: The total cost to hand-produce x large dolls and y small dolls is given by C(x,v) = 2x2 + 4y2 + 4xy…

A: To find x and y that minimizes cost

Q: 41 -5-4-3 2-1 1 2 3 4 5 x y = 3x - 5/3 5 y=-=x+3 3 5 y=-3x - 1²/2 - 3 5 y = -x +3 3

A: As we know that equation of line passing through the points (a,b) and (c,d) is y-b=d-bc-a(x-a)

Q: Minimize z=12x+13y Subject to: 3/2x-3y>or=6 2x+2y>or=14 X>or=0, y>or=0

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Q: Minimize c=2x+10y subject to x+3y > 10,  3x+4y > 20 x,y, >0 using simplex method.

A: The problem is converted to canonical form by adding slack, surplus and artificial variables as…

Q: Maximize Z = 20x1 + 8x2 subject to 16x1 + 8x2 0 %3D

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Q: Minimize c = 5x + y + 5z subject to x + y + z ≥ 80 2x + y ≥ 50 y + z ≥ 50 x ≥ 0, y ≥ 0,…

A: To solve the given linear programming problem: Minimize c = 5x + y + 5z subject to x + y + z ≥ 80…

Q: Question #3 - Find the values of x and y in order to minimize Q if Q=x² +2y² I when x+y = 3.

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Q: Solve the optimization problem. Minimize F = 37x² + 37y2 with xy² = 16. F =

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Q: Construct the dual problem. Minimize  z = – 5x1 – 15x2

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Q: The cost of producing x powerful microcontrollers and y less powerful ones can be approximated by…

A: given: The cost of producing x powerful microcontrollers and y less powerful ones can be…

Q: Minimize and maximize P = 30x+10y subject to 2x + 2y = 4 6x + 4y = 36 2x + y ≤ 10 0 x, y ≥ =

A: The solution is shown in step-2

Q: State the dual problem. Use y₁, y2, y3 and y4 as the variables. Given: y1 ≥ 0, y2 ≥ 0, y3 ≥ 0, and…

A: Introduction: To find the dual of the given linear programing problem we have to change minimization…

Q: 9) A company projects their revenue and cost functions will be R(x) = 3x² + 10x and C(x) = 13 x³ 4x2…

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Q: Find r and h that minimize S subject to the constraint V = 54n.

A: Here V=54π and we should minimize  S=2πrh+2πr2 under the constraint V=54π=πr2h V(r,h)=πr2h-54π