Consider the following LP. Мах z%3D2х, +10х, + бх, subject to X, +2x, + x, = 3 = 4 2x, — х, Xq, X2,X, 2 0 a. Write the associated dual problem. b. Given only the information that the optimal basie variables are x, and x; , (without using simplex method) determine the associated optimal primal and dual solutions.

Q: 4. Solve using Simplex Method: max z = 2x1 - x2 + x3 subject to: 3x1 + x2 + x3 ≤ 60 2x1 + x2 + 2x3 ≤…

A: The given Linear programming problem, maxz=2x1-x2+x3 Subject to,…

Q: 2. Solve the following equation using LU factorization with partial pivoting. + x + 2x, + 2x, = 6 +…

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Q: Find the real solutions of each equation. Verify your results using a graphing utility.

A: 13)  2t-1=1    2t-1=1          2t=1+1          2t=2            t=1 Also, from the graph we have The…

Q: Solve the following LP using the simplex method. Maximize z = 4x1+3x2+6x3 subject to 3x1+x2+3x3 0

A: Given that Maximize z=4x1+3x2+6x3 subject to 3x1+x2+3x3≤302x1+2x2+3x3≤40             x1,x2,x3≥0

Q: Find a value for the constants p and q so that ₁ = 3/2, 72 = 3/2 is the unique optimal solution of…

A: To find the optimal solution of a linear programming problem using graphical method, we first plot…

Q: max z = 3x₁ + Sx25x3 + 8x4 nx1 + x2 + x3 + 3x4 ≤ 7 -x₁- (s+n)x2 - X3 X4-2 X1, X2, X3, X4 20 -

A: (.) Given,           (.) standard form of maximization problem is,        then dual problem is given…

Q: Solve the following LPP using Simplex method.     Max P = 12X + 16Y     Subject to:            10x…

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Q: 2.2. Write the dual formulation of the following model: Maximise 10 x + 13 y Subject to 8 x + 2 y 34…

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Q: 6. Use the simplex method to find the maximum value of subject to + 6x 58 + 12 , X 20.

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Q: Solve by using the simplex method: Maximize: Z = 8х + 3x2 + хз subject to: X1 + 6х2 + 8хз 0, x3 > 0…

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Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: Given the equation of the hyperbola : 3x2-2y2+6x-8y=6.

Q: Q3) Use Simplex Method to Solve the following LP: Maximize_ p = 5x − 4y +3z x +z ≤20 y-z ≤10 subject…

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Q: ¹) solve the following PDE Using method. Y 22x + x 22y = xy the multiplier

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Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: 4. A company manufactures two types of tyres: steel (x) and alloy (y). The revenue functio of the…

A:

Q: 8r 4m Lasmin 10mn 3

A: Let R=4m15m2n-8n10mn3

Q: Consider the following LP. Max z= 5x, +2x, +3x, subject to X, +5x, +2x, = 30 X - 5x, - 6x, < 40 The…

A: The duality principle is the principle that optimization problems may be viewed from either of two…

Q: MAX Z = 9X, +7 X2 UB TO: 2 X1 + 4X2 <40 X1 +3X2 <30 X1 , X220

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Q: A firm produces two types of graphics calculators, x hundreds of type A and y hundreds of type B per…

A: Given: A firm produces two types of graphic calculators of type A and type B.The firm produces x…

Q: Consider the following L.P. Problem: Max.Xo= 3 x1 +12 x2 Subject to: 2x1 + X2 ≤12 3x1 + 4X2 ≥ 21…

A: The given LPP is            Max   X0=3x1+12x2 subject to:           2x1+x2≤123x1+4x2≥21x1≥3x1≥0,…

Q: 5. Use duality to show that the following LP has an optimal solution 2x1 - X2 Subject to 2x, -X2 - X…

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Q: Over what range can the coefficient of x2 vary before the current solution is no longer optimal?…

A: To determine: The range over which the coefficient of x2 can vary before the current solution is no…

Q: Write Hhe system of lineor equalions in tHe {orm A-b ond solve 'this motrix equation for k.…

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Q: Use the simplex method to solve the following z = 3x1 + 3x2 - 9x3 4x1 + 4x2 - 12x3 s 60 5x1 + 5x2 +…

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Q: 3) A company sells two different types of candles, and their profit function for a week is given by…

A: 3) Given that a company sells two different types of candles, and their profit function for a week…

Q: Solve graphically the dual of the LLP Minimise: z=4w; +6w,+5w,-W4 Sub. to w, +w, 23 W; +w, –w,2-2…

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Q: Variant 1: F%3D 3x, + 2x, тах Х, + 2x, < 6 2х1 + х2 < 6

A: Max F=3x1+2x2 Subject to x1+2x2

Q: P.Draw or solve the following graphically: 3x1 + 4x2 Xq + 2x2s 16 2x, + 3x2 s 18 Xq 22 Max z = s.t.…

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Q: 2. Solve the following LPP using Simplex method. Max P 12X + 16Y Subject to: 10x + 20y =0 and Y >= 0

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Q: 4. For each given solution, identify all + signs (if any) that are false. Explain why. x2 + 6 = 66…

A: (a) look like true but (b) is false. There is error in the last line. Correct solution is…

Q: min 4a1 + 5xз 2x1 + x2 – 53 -3x1 subject to = 1 + 4x3 + x4 = 2 X; 2 0, i = 1, 2, 3, 4.

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Q: Given that fx) = 2r-3 and g(r) = 9x²-5x+11, determine the following: a. g(x) – Ax) = b. flx) • g(x)…

A: Given that…

Q: 6. Determine the maximum value of the following quadratic function. fx) = -3 x2 + 6x + 4 %3D О Мах…

A: To find the maximum value of f(x).

Q: Solve this LP max z = 3x₁ + 2x₂ +2.5x3 8.t. 1 + 2 + 2003 201 + 2x3 1, 2, 3 > 0 has optimal tableau…

A: Given that the linear programming problem:        max z=3x1+2x2+2.5x3,s.t.         x1+x2+2x3≤4,…