(a) Minimize 2x1 +4x2 – 4x3 +7x4 subject to 8x1 2x2 + x3 –- X4 < 50 3x1 + 5x2 + 2x4 < 150 X1 - x2 + 2x3 – 4x4 < 100 X1,X2,X3, X4 >0

Q: 14. Maximize P = 15x1 + 20x2 %3D subject to 2xı + x2 s 9 X1 + x2 s 6 X1 + 2r2 s 10 X1, X2 0

A:

Q: Minimize f = 4x1 - 10x2 - 20x3 subject to 3x1 + 4x2 + 5x3 < 60, 2x1 + x2 < 20, 2x1 + 3x3 < 30

A:

Q: Find solution using LINGO Maximize Z = 6x1 - 4x2 subject to 2 x1+ 4 x2 = 16 and x1, x2 >= 0

A:

Q: 32. Maximize and Minimize Z = 7x + 36y 2x + 3y > 6 -3x+ 4y < 8 5x – y < 15 Subject to :

A: We first draw 2x+3y=6 , -3x+4y=8 and 5x-y=15(using graphing calculator)

Q: Solve using the Graphical Method: Minimize z = 3x, + &x2 subject to X1 + x2 2 8 2x, – 3x2 s 0 xị +…

A:

Q: 1. A cable wire 100 meters long is to be cut into two pieces. One of the pieces will be bent into…

A: Let length of one part is x  Therefore length of another part is (100-x)

Q: Q3/ Use the graphical method to solve the following LP problem. Minimize Z=-x, + 2x₂ subject to the…

A:

Q: c) Maximize Z = 3x1+ 4x2+ 2x3 subject to: X1+ 2x2 + 0x3 s 10 2x1 + 2x2 + x3< 10 X1, X2, X3 20 d)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2. Minimize Z = 4X1 + 4X2 + 2X3 Subject to X1 + 3X2 +6X3 >= 400 2X1 +6X2 + 4X3 >= 350 2X1 + 8 X2 + 5…

A: The LPP is solved using excel solver and all the steps are mentioned.

Q: Maximize and minimize p = x + 2y subject to x + y > 2 x + ys 10 х — уs 2 х — у2 -2.

A:

Q: minimize Z = 8x, + 2x2 subject to 2x, - 6x2 s 12 5x1 + 4x2 2 40 X1 + 2r, 2 12 X2 S 6 X1, X2 0

A:

Q: 2. Minimize: Z = 20X₁ + 10X₂ + 80X3 Subject to: X₁ + X₂ + X3 ≥ 6 : 2X₁ + 4X₂ + X3 = 20 2X₁ + X₂ ≤ 5…

A: We have to find the solution to the given problem.

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: 5x, + 3x2 2x, + 5x2 2 10 3x + x22 6 X + 7x2 2 7 Minimize subject to and x 20, x2 2 0.

A: We use graphical method to solve the given problem Minimize 5x1+3x2 Subject to 5x1+3x2 ≥10   3x1+…

Q: Solve by the Big M – method: Maximize Ζ = x1 + 2x2 + 3x3 − x4 Subject to x1 + 2x2 + 3x3 = 15 2x1 +…

A:

Q: 4) A manufacturer has determined that the total cost C of operating a factory is C = 0.5x^2 + 15x +…

A: Given, Total cost C of operating a factory is C=0.5x2+15x+5000.  where x is the number of units…

Q: f) Minimize Z = 5x1 + 4x2 subject to: -4x1 + 3x2 2 -10 8x1- 10x2 s 80 X1, X2 2 0

A:

Q: Minimize ƒ = x² + x² +60x, subject to the constraints 8₁x₁-8020 8₂x₁+x₂-120≥0 using Kuhn-Tucker…

A:

Q: Maximize P=5x1+6x2+4x3   Subject to: x1+2x2≤6 5x1+3x2+3x3≤24 x1,x2,x3≥0

A:

Q: 12) A manufacturer has determined that the total cost C of operating a factory is C= 3x² + 70x +…

A: We have given: The total cost C(x) = 3x2 + 70x + 2700, where x is the number of units produced.

Q: 7. Minimize C=5x+2y x+3 y215 Subject to 2 x+ y2 20 x, y20

A: Find the attachment

Q: c) Maximize Z = 3x1+ 4x2+ 2x3 subject to: X1 + 2x2 + 0x3 < 10 2x1 + 2x2 + X3 S 10 X1, X2, X3 2 0 d)…

A: Note: We are entitled to solve one question at a time. As the specified one is not mentioned, So we…

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

A: The given LPP is  Minimize Z=3X1+5X2+5X3+4X4subject to 8X1+2X4≤1004X2+3X3=90X1,X2,X3,X4≥0 Add the…

Q: 34. Minimize and maximize P = 12x + 14y subject to -2x + y 2 6 x + ys 15 3x - y 2 0 x, y 2 0

A: Given, minimize, and maximize                P=12x+14y     subject to              -2x+y≥6…

Q: Consider the problem f (x) subject to g;(x) = 0, minimize %3D

A: Given, the problem                 minimise f(x)            subject to   gi(x)=0, i=1, . . ., l…

Q: maximize z=8.50x1+12.10x2 subject to 2x1+3x2 <  24,000 x1 < 6,600 x2 < 5,500 x1+x2 < 10,000

A: topic- linear programming

Q: Minimize f = x²+x+60x, subject to the constraints 8₁x₁-8020 82x₁+x₂-120≥0 using Kuhn-Tucker…

A: Given - To minimize f=x21+x22+60x1  subject to constraints g1=x1-80≥0g2=x1+x2-120≥0 We have to…

Q: (a) Maximize z = 2x1 – 4x2 + 5x3 – 6x4 subject to X1 + 4x2 – 2xz + 8x4 0

A: ⊙ Given LPP is Maximize τ = 2x1-4x2+5x3-6x4sub to. x1+4x2-2x3+8x4 ≤2-x1+2x2+3x3+4x4 ≤1Now, we…

Q: Minimize -z=-8 X1 – 10 X2 -7X3 Subject to XI +3 X2+ 2X3 < 10 -XI -5 X2 - X32 -8 XI, X2, X3 20

A:

Q: Z = 2x + 3y   Subject to –2x – y ≥ –10 x + 3y ≥  6 x ≥ 0 y ≥  0

A: To maximise the equation Z=2x+3y, the equations -2x-y≥-10 and x+3y≥6 are to be graphed and shaded.…

Q: Let fo(r1, x2) = x} + 4x3. Find the optimal point and the optimal value of the convex optimization…

A:

Q: _2. Solve the problem minimize f(x) = -xỉ +x3 – x,x2 subject to 2x1 – x2 > 2 X1 + x2 0. |

A:

Q: Maximize p = x + y subject to x + 3y ≤ 8 3x + y ≤ 8 x ≥ 0, y ≥ 0.

A: Solve LINEAR PROGRAMMING Problem by using graphical method

Q: minimize c= -x+2y subject to y or equal to 4 x> or equal to 6 x+ y < or equal to 16

A:

Q: Minimize Z=-x₂ + 2x₂ subject to the constraints and (1-x₂ + 3x₂ ≤9 x.x₂ 20. (11) x₂ + x₂ ≤ 6. (11)…

A:

Q: Maximize p = x + 2y subject to x + 4y ≤ 22 4x + y ≤ 13 x ≥ 0, y ≥ 0.

A:

Q: 5. Maximize z = 3x, + x2 + 4x3 subject to 3x, + 3x2 + xz < 18 2x1 + 2x2 + 4xz = 12 %3D X1 2 0, x3 2…

A: We to convert the given linear programming problem in to dual problem. The solution is explained…

Q: Suppose a manufacturer has determined that the total cost C of operating a factory is C =0.4x² + 17x…

A:

Q: A manufacturer has determined that the total cost C of operating a factory is C = 1.5x2 + 45x +…

A: Given that the cost function is C = 1.5x2 + 45x + 15000. So the average cost function is A=Cx=1.5x2…

Q: Use the Lagrange multiplier method to solve Minimize z = x} + x + x Subject to x, + 2x, + 3x3 = 7…

A: We have to solve the following problem using the Lagrange multiplier, Min z=x12+x22+x32 Subject to :…

Q: Maxcimize and Minimize Z= 2x+9y subject to: 9x +4y 2 36 9x-6y 2 0 y 56 xy20

A: Given ,  Linear programming problem Maximize and Minimize Z = 2x + 9y  Subject to :  9x + 4y ≥ 36 9x…

Q: Solve the optimization problem. Maximize P = xyz with x +z = 18 and y +z = 18, and x, y, and z 2 0.…

A: NOTE: Refresh your page if you can't see any equations. . the first constraint is  . the second…

Q: 1. Minimize z = 3x1 + 4x2 subject to x; + 4x2 > 8 2x1 + 3x2 2 12 2x, + x2 2 6 х, 2 0, х, 2 0. 2.…

A:

Q: Determine the reduced objective and the reduce problem at point x = (0.6, 0.4): Minimize f(x) = (x₁…

A: A mathematical method called a linear programming problem (LPP) is used to maximise or reduce the…

Q: Use the simplex method to solve the following problem and verify the solution by the graphical…

A:

Q: 3. Minimize: Z = 40X₁ + 80X2 + 50X3 Subject to: X₁ + 2X₂ + 3X3 ≥ 18 X₁ + 4X₂ + X3 ≥ 60 2Y 6Y A. Y…

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

Q: Maximize Subject to · P= 30x +4082 2x₁+x₂ ≤ 30 X₁ + X₂ ≤21 *₁+2x₂ ≤ 36 X₁ X₂ 20

A:

Q: 2. Minimize: Z 20X1 + 10X2 + 80X3 %3D Subject to: X1 + X2 + X3 > 6 2X1 + 4X2 + X3 = 20 2X1 + X2 < 5…

A: We have to find the solution to the given problem.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: