5. Maximize z = 3x, + x2 + 4x3 subject to 3x, + 3x2 + xz < 18 2x1 + 2x2 + 4xz = 12 %3D X1 2 0, x3 2 0. 6. Minimize z = 5x, + 2x2 + 6x3 subject to 4x, + 2x, + X3 z 12 3x, + 2x2 + 3x356 X1 2 0, x2 2 0.
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: Given the LP problem: Maximize Z = 3X1 +5X2, Subject to: X1 + 2X2 ≤ 50, - X1 + X2 ≥ 10, X1 ≥ 0 X2 ≥…
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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: 1. Maximize z= 3x + 7y subject to %3D 3x – 2y 0, y>0.
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Q: Solve the following boundary value problem by the method of separation of variables:
A: In this question, we have to solve the BVP δuδt=δ2uδt2withu(0,t)=0 =u(4,t)u(x,0)=6sin(πx2)+3sin(πx)…
Q: find the values of x greater than or equal to 0 y greater than or equal to 0 that maximize…
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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: Graph the feasible region. x + y 2 3 -x + y 2 1
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Q: 1. Maximize: Z = 50X, + 100X; + 150X, Subject to: 2X, + 2X2 s 200 3X, s 150 4X, + 4X3 5 600 X,2 0,…
A: Now we will find the solution using Simplex method
Q: Suppose the feasible region has four corners at these points (0,0), (8,0), (0,12), and (4,8). If…
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Q: 8. Maximize Z = 0.5x –0.3y Subject to x- y >-2, 2x - y<4, 2x+ y = 8, *** x, y 2 0.
A:
Q: Graph the following solution set, and determine the feasible region in graph. Also determine…
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Q: 7. Minimize C=5x+2y x+3 y215 Subject to 2 x+ y2 20 x, y20
A: Find the attachment
Q: 4. Maximize Z = 3x1 + 2x2 + x3 Subject to 2x1 +x2 + x3 < 150 2x1 + 2x2 + 8x3 < 200 2x1 + 3x2 + x3 5…
A: maximise Z= 3x1+2x2+x3 subject to 2x1+x2+x3≤150 2x1+2x2+8x3≤200 2x1+3x2+x3≤320 x1,x2,x3≥0 adding the…
Q: Given the LP problem: Maximize Z = 3X1 + 5X2, Subject to: X1 + 2X2 10, X1 > 0 X2 > 0,
A:
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 4X + 9Y, constraints: 5X + 3Y s 30, 7X • 2Y s 28, X 2 0, Y 2 0
A: Given constraints are 5x+3y≤30 and 7x+2y≤28, x≥0,y≥0. Draw the given inequalities and obtain the…
Q: Maximize p = 5x − 4y + 3z subject to 10x + 10z ≤ 100 5y − 5z ≤ 50 10x − 5y ≤ 50 x ≥ 0, y ≥ 0, z ≥…
A:
Q: Maximize p = 5x − 4y + 3z subject to 2x + 2z ≤ 100 5y − 5z ≤ 50 2x − 5y ≤ 50 x ≥ 0, y ≥ 0, z ≥ 0.…
A:
Q: 2. Use Lagrange multipliers to maximize f(, y) = x + 3ry + 4y subject to the constraint 2x + y = 1.
A: We use Lagrange multipliers method
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: LPP by the graphical method. minimize 20x1+10x2 subject to x1 + 2x2 ≤40, 3x1 + x2 ≥30, 4x1 + 3x2…
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Q: Solve the LPP by using Big M method Maximize z = x1 + 5x2 subject to 3x1 + 4x2 s6 x1 + 3x2 2 2 x1,…
A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…
Q: Maximize z = 10x₁ + 55x2 + 50x3, subject to 16x1 4x2+ 9x3 S 122 8x₁ + 13x2 + 22x3 ≤ 142 6x215x3 S…
A:
Q: Maximize z=14x, + 3x2 subject to: 7x, + 3x, 58 X1 +3x, 54 X, 20, X2 2 0. with
A: We will be using the simplex method to solve the following system.
Q: 1. Minimize z = 3x, + 4x2 subject to x, + 4x2 > 8 2x1 + 3x2 2 12 2х, + х, 2 6 х, 20, х, 2 0. 2.…
A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…
Q: It has been said each LP problem that has a feasible region has an infinite number of solutions?…
A: In each LPP, since the feasible region is continuous, and if we can consider accepting non-integer…
Q: こッt dss txs 3x,+6x27X L27 X, + Yx2 +3x, E 14 X,Z0, X2 30,Xs ZO MAximize 2x2 2. eubJect to
A: The given problem is Maximize z=4x1+2x2+x3 Subject to 3x1+4x2+x3≤27x1+4x2+3x3≤14x1,x2,x3≥0
Q: Minimize 8x, +10x, +7x, +6x,+11x, +9x6 Subject to 12.x, + 9x, +25x, +20x; +17x, +13x, 2 60 35x,…
A: We solve this LPP by dual simplex method.
Q: 9. Maximize subject to 2x + 7x2 -2x, + x2S-4 X - 2x S-4 and x 2 0, x2 2 0.
A: 9 Given Maximize Z=2x1+7x2 Subject to −2x1+x2≤−4x1−2x2≤−4 And x1≥0, x2≥0 Solve equation −2x1+x2=−4…
Q: Number 40
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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: Consider the following Scenario: • Maximize z = 9x1 + 12x2 + 11x3 o Subject to 6x1 + 4x2 + X3 s 20…
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Q: 2.6 Convert the original LP problem into LP standard form. maximize ) = -x, + 2x2 - x3 + 3x4 s.t. X1…
A: The given problem is to convert the given original linear programming problem to the standard form…
Q: 18. Maximize P = 4x – y subject to 2x – 3y 2 -6 2x + y < 6 x + 3y 2 3
A:
Q: 6. Maximize z-x, + 2x2 + 3x3 + x4 subject to 2x, + x, + x, + 2x, s 18 3x, +5x2+ 2x,+ 3x, s24 3x, +…
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Q: Solve Beaver Creek Pottery Company problem (in Ch. 2). Maximize Z = $40x1 + $50x2 subject to 1x1 +…
A:
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.…
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Q: Maximize 2x1 + x2 – 3r3 + 5x4 subject to xi + 2r2 + 2r3 + 4x4 < 40 2x1 – r2 + 13 + 2x4 < 8 4x1 – 2x2…
A:
Q: 6. In Genshin Impact, the optimal crit rate z to crit damage y ratio can be obtained by maximizing 2…
A: We have the following optimization problem : maximize : z = xy constraint : x + y/2 = 100
Q: 2. Find the duals. a) Maximize Z = 2x₁ + x2-x3 subject to: 2x1 + 2x2 ≤3 -X1 + 4x2 + 2x3 ≤ 5 X1, X2,…
A: Primal to dual conversion Objective function is maximize is converted to minimize Objective…
Q: Solve the LP problem. If n op lo ou Maximize p =x-2y subject t x+2ys 7 05 y 5x-4y 2 0 x2 0, y 2 0.…
A: Given linear programing problem is Maximize p=x−2y Subject to x+2y≤7x−5y≤05x−4y≥0 and x≥0,y≥0. Draw…
Q: 2. Minimize z - 6х, + 6х, + 8x, + 9х, subject to X, + 2xz + x3 + x4 2 3 2x, + x3 + 4x3 + 9x4 2 8 X,…
A: Given- Minimize Z = 6x1 + 6x2 + 8x3 + 9x4subject tox1 + 2x2 + x3 + x4 ≥ 32x1 + x2 + 4x3 + 9x4 ≥ 8x1…
Q: Minimize : 6y+4y2+2y3 2yı +2y2 +y3 2 2 yi +3y2 +2y3 2 3 Yi +y2 +2y3 2 4
A: For convenience, we take y_1=x_1, y_2=x_2 and y_3=x_3.
Q: A restaurant requires different numbers of full-time employees on different days of the week. Union…
A: Linear Programming model is used to understand the most optimal solution based on the constraints.…
Q: A diabetic patient needs at least 30 units of vitamin A, at least 45 of vitamin C, and at least 30…
A: Let x and y denote the number of brand X and brand Y capsules daily taken respectively. Cost of…
Q: In Genshin Impact, the optimal crit rate x to crit damage y ratio can be obtained by maximizing the…
A: For relative maximum or minimum To maximize or minimize a function f(x) 1st we need to find its…
Q: Maximize p = 5x + 7y + 6z subject to x + y + z 100 x 2 0, y 2 0, z > 0. p = (х, у, 2) 3
A: The given constraints are, x+y+z≤150, x+y+z≥100 and x≥0, y≥0, z≥0. Obtain the coordinates x,y,z…
Q: 28. Minimize and maximize z = 400x + 100y %3D subject to 3x + y 24 x +y 16 x + 3y 2 30 x, y > 0
A:
find the dual of the given linear programming problem
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- Minimize and maximizez=30x+20ySubject to 3x+y≥36x+y≥24x+3y≥30x, y≥0A 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. $993,000Minimize z=12x+13y Subject to: 3/2x-3y>or=6 2x+2y>or=14 X>or=0, y>or=0
- 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.Determine the number of slack variables required. Maximize z=15x1+7x2 subject to: 2x1+6x2≤20 15x1+x2 ≤50 4x1 + 15x2 ≤ 125 with x1≥0, x2≥0.2. Maximise 1170x1 + 1110x2Subject to: 9x1 + 5x2 ≥ 5007x1 + 9x2 ≥ 3005x1 + 3x2 ≤ 15007x1 + 9x2 ≤ 19002x1 + 4x2 ≤ 1000x1, x2 ≥ 0-Find graphically the feasible region and the optimal solution.
- Find the values of x, y, and z that maximize xyz subject to the constraint 192−x−8y−16z=0. x=_________?A company can sell all it produces of a given output for$2/unit. The output is produced by combining two inputs. Ifq1 units of input 1 and q2 units of input 2 are used, then the company can produce q1/31q2/32 units of the output. If it costs$1 to purchase a unit of input 1 and $1.50 to purchase a unitof input 2, then how can the company maximize its profit?Find the multiple solutions.Maximize z = 45x1 + 30x2, subject to 2x1 + 9x2 ≤ 144 2x1 + 3x2 ≤ 60 3x1 + 2x2 ≤ 75 x1 ≥ 0, x2 ≥ 0 z = at ( , 0), ( , ), and on the line segment between.
- A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and square. What should the wire be cut to (a) maximize and (b) minimize the combined area of the circle and the square?Suppose the feasible region has four corners at these points (0,0), (8,0), (0,12), and (4,8). If the profit formula is P = $2x + $4y, what is the maximum profit possible?To minimize costs on the production line, an industrial engineer at a fiber-optic manufacturing firm is considering two robots. Robot X would have a $82,000 first cost, a $30,000 annual maintenance and operation (M&O) cost, and $50,000, $42,000, and $35,000 salvage prices after 1, 2, and 3 years, respectively. Robot Y will have a first cost of $97,000, a yearly M&O cost of $27,000, and after 1, 2, and 3 years, respectively, salvage prices of $60,000, $51,000, and $42,000. If a 2-year study period is specified at an interest rate of 15 percent per year and replacement after 1 year is not an option, what robot should be selected?